Solve the initial value problem for y as a function of x.
-$$\left( x ^ { 2 } + 49 \right) \frac { d y } { d x } = 1 , y ( 7 ) = 0$$
A) $y = \frac { 1 } { 7 } \tan ^ { - 1 } \frac { x } { 7 } - \frac { \pi } { 28 }$
B) $y = \frac { 1 } { 7 } \tan ^ { - 1 } \frac { x } { 7 }$
C) $y = \frac { x } { 7 } - 1$
D) $y = \frac { 1 } { 7 } \sin ^ { - 1 } \frac { x } { 7 } - \frac { \pi } { 14 }$

Question

Quizplus · Accepted Answer

The differential equation can be solved by separating variables and integrating. The integration results in an inverse tangent function, and the initial condition is used to determine the constant of integration.

Solve the Initial Value Problem for Y as a Function (x2+49)dydx=1,y(7)=0\left( x ^ { 2 } + 49 \right) \frac { d y } { d x } = 1 , y ( 7 ) = 0(x2+49)dxdy​=1,y(7)=0

Solve the Initial Value Problem for Y as a Function $\left( x ^ { 2 } + 49 \right) \frac { d y } { d x } = 1 , y ( 7 ) = 0$