Deck 17: Second-Order Differential Equations

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سؤال
Suppose a spring has mass M and spring constant k and let <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . Suppose that the damping constant is so small that the damping force is negligible. If an external force <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.

A) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
A series circuit consists of a resistor <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , an inductor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , a capacitor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , and a <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

A) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> m/s, find the position x(t) of the mass after t seconds.

A) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A spring with a mass of 2 kg has damping constant 14, and a force of A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.<div style=padding-top: 35px> N is required to keep the spring stretched A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.<div style=padding-top: 35px> m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.
سؤال
A spring with a mass of <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> kg has damping constant 28 and spring constant <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> . Find the damping constant that would produce critical damping.

A) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px>
B) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> 9 <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px>
C) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px>
D) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px> <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px>
E) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A series circuit consists of a resistor <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , an inductor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , a capacitor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , and a generator producing a voltage of <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> If the initial charge is <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and the initial current is 0, find the charge <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> at time t.

A) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A spring has a mass of <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px> kg and its damping constant is <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px> . The spring starts from its equilibrium position with a velocity of <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px> m/s. Graph the position function for the spring constant <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px> .

A) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px>
B) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px>
C) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   <div style=padding-top: 35px>
سؤال
A spring with a mass of 2 kg has damping constant 14, and a force of A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. Find the mass that would produce critical damping.<div style=padding-top: 35px> N is required to keep the spring stretched A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. Find the mass that would produce critical damping.<div style=padding-top: 35px> m beyond its natural length. Find the mass that would produce critical damping.
سؤال
The figure shows a pendulum with length L and the angle <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> from the vertical to the pendulum. It can be shown that <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , as a function of time, satisfies the nonlinear differential equation <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> where <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> we can use the linear approximation <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A spring with a <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> -kg mass has natural length <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> m and is maintained stretched to a length of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> m by a force of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> N. If the spring is compressed to a length of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> m and then released with zero velocity, find the position <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> of the mass at any time <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The solution of the initial-value problem <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.

A) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A series circuit consists of a resistor A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.<div style=padding-top: 35px> an inductor with L = A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.<div style=padding-top: 35px> H, a capacitor with
C = A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.<div style=padding-top: 35px> F, and a A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.<div style=padding-top: 35px> -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.
سؤال
A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.

A) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)   <div style=padding-top: 35px>
B) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)   <div style=padding-top: 35px>
C) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Use power series to solve the differential equation.. <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem using the method of undetermined coefficients. Solve the initial-value problem using the method of undetermined coefficients.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem using the method of undetermined coefficients. Solve the initial-value problem using the method of undetermined coefficients.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.  <div style=padding-top: 35px>
سؤال
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.  <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Graph the particular solution and several other solutions. <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)   <div style=padding-top: 35px>

A) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)   <div style=padding-top: 35px>
B) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)   <div style=padding-top: 35px>
C) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)   <div style=padding-top: 35px>
سؤال
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the boundary-value problem, if possible. <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>

A) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
B) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
C) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
D) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
E)No solution
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
E)None of these
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find f by solving the initial value problem. <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> ; <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> , <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px>

A) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> + 4 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> x - 10
B) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> + 2 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> x <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px>
C) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> + 4 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> x - 5
D) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> + 2 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px> x <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these <div style=padding-top: 35px>
E)None of these
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Solve the initial value problem. Solve the initial value problem.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the boundary-value problem, if possible. <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>

A) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
B) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
C) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
D) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution <div style=padding-top: 35px>
E)No solution
سؤال
Solve the boundary-value problem, if possible. Solve the boundary-value problem, if possible.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Solve the boundary-value problem, if possible. Solve the boundary-value problem, if possible.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
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Deck 17: Second-Order Differential Equations
1
Suppose a spring has mass M and spring constant k and let <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   . Suppose that the damping constant is so small that the damping force is negligible. If an external force <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.

A) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)
B) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)
C) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)
D) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)
E) <strong>Suppose a spring has mass M and spring constant k and let   . Suppose that the damping constant is so small that the damping force is negligible. If an external force   is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.</strong> A)   B)   C)   D)   E)
2
A series circuit consists of a resistor <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   , an inductor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   , a capacitor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   , and a <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

A) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)
B) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)
C) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)
D) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)
E) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a   -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.</strong> A)   B)   C)   D)   E)
3
A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)   m/s, find the position x(t) of the mass after t seconds.

A) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)
B) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)
C) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)
D) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)
E) <strong>A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of   m/s, find the position x(t) of the mass after t seconds.</strong> A)   B)   C)   D)   E)
4
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
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5
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
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6
A spring with a mass of 2 kg has damping constant 14, and a force of A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t. N is required to keep the spring stretched A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t. m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.
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7
A spring with a mass of <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   kg has damping constant 28 and spring constant <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   . Find the damping constant that would produce critical damping.

A) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)
B) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   9 <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)
C) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)
D) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)   <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)
E) <strong>A spring with a mass of   kg has damping constant 28 and spring constant   . Find the damping constant that would produce critical damping.</strong> A)     B)   9   C)     D)     E)
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8
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
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9
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
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10
A series circuit consists of a resistor <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   , an inductor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   , a capacitor with <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   , and a generator producing a voltage of <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   If the initial charge is <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   and the initial current is 0, find the charge <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)   at time t.

A) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)
B) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)
C) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)
D) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)
E) <strong>A series circuit consists of a resistor   , an inductor with   , a capacitor with   , and a generator producing a voltage of   If the initial charge is   and the initial current is 0, find the charge   at time t.</strong> A)   B)   C)   D)   E)
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Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
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A spring has a mass of <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   kg and its damping constant is <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   . The spring starts from its equilibrium position with a velocity of <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   m/s. Graph the position function for the spring constant <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)   .

A) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)
B) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)
C) <strong>A spring has a mass of   kg and its damping constant is   . The spring starts from its equilibrium position with a velocity of   m/s. Graph the position function for the spring constant   .</strong> A)   B)   C)
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A spring with a mass of 2 kg has damping constant 14, and a force of A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. Find the mass that would produce critical damping. N is required to keep the spring stretched A spring with a mass of 2 kg has damping constant 14, and a force of   N is required to keep the spring stretched   m beyond its natural length. Find the mass that would produce critical damping. m beyond its natural length. Find the mass that would produce critical damping.
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The figure shows a pendulum with length L and the angle <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   from the vertical to the pendulum. It can be shown that <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   , as a function of time, satisfies the nonlinear differential equation <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   where <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   we can use the linear approximation <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)   <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)

A) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)
B) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)
C) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)
D) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)
E) <strong>The figure shows a pendulum with length L and the angle   from the vertical to the pendulum. It can be shown that   , as a function of time, satisfies the nonlinear differential equation   where       we can use the linear approximation            </strong> A)   B)   C)   D)   E)
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A spring with a <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   -kg mass has natural length <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   m and is maintained stretched to a length of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   m by a force of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   N. If the spring is compressed to a length of <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   m and then released with zero velocity, find the position <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   of the mass at any time <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)   .

A) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)
B) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)
C) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)
D) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)
E) <strong>A spring with a   -kg mass has natural length   m and is maintained stretched to a length of   m by a force of   N. If the spring is compressed to a length of   m and then released with zero velocity, find the position   of the mass at any time   .</strong> A)   B)   C)   D)   E)
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16
The solution of the initial-value problem <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.

A) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)
B) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)
C) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)
D) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)
E) <strong>The solution of the initial-value problem   is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.</strong> A)   B)   C)   D)   E)
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17
A series circuit consists of a resistor A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. an inductor with L = A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. H, a capacitor with
C = A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. F, and a A series circuit consists of a resistor   an inductor with L =   H, a capacitor with C =   F, and a   -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.
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18
A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.

A) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)
B) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)
C) <strong>A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.</strong> A)   B)   C)
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19
Use power series to solve the differential equation. <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation.  </strong> A)   B)   C)   D)   E)
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20
Use power series to solve the differential equation.. <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)

A) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)
B) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)
C) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)
D) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)
E) <strong>Use power series to solve the differential equation..  </strong> A)   B)   C)   D)   E)
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21
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.
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22
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
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23
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
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24
Solve the differential equation. Solve the differential equation.
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25
Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.
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26
Solve the initial-value problem using the method of undetermined coefficients. Solve the initial-value problem using the method of undetermined coefficients.
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27
Solve the initial-value problem using the method of undetermined coefficients. Solve the initial-value problem using the method of undetermined coefficients.
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28
Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.
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29
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)

A) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
B) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
C) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
D) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
E) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
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30
Solve the differential equation using the method of undetermined coefficients. <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of undetermined coefficients.  </strong> A)   B)   C)   D)   E)
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31
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.
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32
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.
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33
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
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34
Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.
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35
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
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36
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)

A) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
B) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
C) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
D) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
E) <strong>Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.  </strong> A)   B)   C)   D)   E)
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37
Solve the differential equation. Solve the differential equation.
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38
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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39
Graph the particular solution and several other solutions. <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)

A) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)
B) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)
C) <strong>Graph the particular solution and several other solutions.  </strong> A)   B)   C)
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40
Solve the differential equation using the method of variation of parameters. <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation using the method of variation of parameters.  </strong> A)   B)   C)   D)   E)
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41
Solve the boundary-value problem, if possible. <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution

A) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
B) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
C) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
D) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
E)No solution
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42
Solve the initial-value problem. <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.   .</strong> A)   B)   C)   D)   E)
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43
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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44
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)None of these
E)None of these
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45
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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46
Find f by solving the initial value problem. <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   ; <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   , <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x

A) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   + 4 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   x - 10
B) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   + 2 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   x <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x
C) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   + 4 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   x - 5
D) <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   + 2 <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x   x <strong>Find f by solving the initial value problem.   ;   ,  </strong> A)         + 4     x - 10 B)         + 2     x   C)         + 4     x - 5 D)         + 2     x
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47
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)None of these
E)None of these
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48
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
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49
Solve the differential equation. Solve the differential equation.
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50
Solve the differential equation. Solve the differential equation.
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51
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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52
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
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53
Solve the differential equation. Solve the differential equation.
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54
Solve the initial-value problem. Solve the initial-value problem.
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55
Solve the initial-value problem. Solve the initial-value problem.
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56
Solve the initial value problem. Solve the initial value problem.
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57
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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58
Solve the boundary-value problem, if possible. <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution

A) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
B) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
C) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
D) <strong>Solve the boundary-value problem, if possible.  </strong> A)   B)   C)   D)   E)No solution
E)No solution
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59
Solve the boundary-value problem, if possible. Solve the boundary-value problem, if possible.
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60
Solve the differential equation. Solve the differential equation.
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61
Solve the boundary-value problem, if possible. Solve the boundary-value problem, if possible.
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62
Solve the initial-value problem. Solve the initial-value problem.
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63
Solve the differential equation. Solve the differential equation.
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