Deck 9: First-Order Differential Equations

Question 1

Solve. Round your results to four decimal places.

Answer 1

B

Question 2

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Answer 2

D

Question 3

Solve. Round your results to four decimal places.
Use the Euler method with dx = 0.2 to estimate y(3) if and y(2) = -2. What is the exact value of y(3)?

Answer 3

D

Question 4

Match the differential equation with the appropriate slope field.

Question 5

Match the differential equation with the appropriate slope field.

Question 6

Match the differential equation with the appropriate slope field.

Question 7

Question 8

Match the differential equation with the appropriate slope field.

Question 9

Question 10

Match the differential equation with the appropriate slope field.

Question 11

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Question 12

Question 13

Question 14

Match the differential equation with the appropriate slope field.

Question 15

Solve. Round your results to four decimal places.

Question 16

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Question 17

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Question 18

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Question 19

Use Euler's method to calculate the first three approximations to the given initial value problem for the specified
increment size. Round your results to four decimal places.

Question 20

Question 21

Solve the differential equation.

Question 22

Solve the problem.
Using the given conditions, obtain a slope field and graph the particular solution over the specified interval.
Then find the general solution of the differential equation.

Question 23

Solve the differential equation.

Question 24

Solve the initial value problem.

Question 25

Solve the initial value problem.

Question 26

Solve the differential equation.

Question 27

Solve the differential equation.

Question 28

Solve the differential equation.

Question 29

Use Euler's method with the specified step size to estimate the value of the solution at the given point x*. Find the value
of the exact solution at x*.

Question 30

Solve the differential equation.

Question 31

Solve the differential equation.

Question 32

Use Euler's method with the specified step size to estimate the value of the solution at the given point x*. Find the value
of the exact solution at x*.

Question 33

Solve the differential equation.

Question 34

Solve the initial value problem.

Question 35

Solve the problem.
Using the given conditions, obtain a slope field, solve for the general solution, and plot solution curves for the
arbitrary constant values C = -2, 2, and 4.

Question 36

Solve the differential equation.

Question 37

Solve the initial value problem.

Question 38

Solve the problem.
Using the given conditions, obtain a slope field and graph the particular solution over the specified interval.
Then find the general solution of the differential equation.

Question 39

Use Euler's method with the specified step size to estimate the value of the solution at the given point x*. Find the value
of the exact solution at x*.

Question 40

Solve the differential equation.

Question 41

A) 8.01 min
B) 6.01 min
C) 5.01 min
D) 7.01 min

Question 42

Solve the initial value problem.

Question 43

Solve the differential equation.

Question 44

Determine which of the following equations is correct.

Question 45

Solve the problem.
dy/dt = ky + f(t) is a population model where y is the population at time t and f(t) is some function to describe the net effect on the population. Assume k = .02 and y = 10,000 when t = 0. Solve the differential equation of y
When f(t) = -17t.

Question 46

Solve the differential equation.

Question 47

A 100 gal tank is half full of distilled water. At time = 0, a solution containing 2 lb/gal of concentrate enters the tank at the rate of 4 gal/min, and the well-stirred mixture is withdrawn at the rate of 3 gal/min. When the tank
Is full, how many pounds of concentrate will it contain?

A) 175 pounds
B) 200 pounds
C) 187.5 pounds
D) 150 pounds

Question 48

Solve the initial value problem.

Question 49

Solve the problem.
A tank initially contains 120 gal of brine in which 40 lb of salt are dissolved. A brine containing 4 lb/gal of salt runs into the tank at the rate of 8 gal/min. The mixture is kept uniform by stirring and flows out of the tank at
The rate of 5 gal/min. Write, in standard form, the differential equation that models the mixing process.

Question 50

Solve the differential equation.

Question 51

Solve the differential equation.

Question 52

A tank contains 100 gal of fresh water. A solution containing 2 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out of the tank at the rate of 2 gal/min. Find the
Maximum amount of fertilizer in the tank and the time required to reach the maximum.

A) 48 pounds, 60 minutes
B) 48 pounds, 40 minutes
C) 60 pounds, 40 minutes
D) 50 pounds, 50 minutes

Question 53

Solve the differential equation.

Question 54

Solve the initial value problem.

Question 55

How many seconds after the switch in an RL circuit is closed will it take the current i to reach 40% of its steady state value? Express answer in terms of R and L and round coefficient to the nearest hundredth.

A) 0.92 L/R seconds
B) 0.51 L/R seconds
C) 1.12 L/R seconds
D) 0.71 L/R seconds

Question 56

Solve the problem.
A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at
The rate of 3 gal/min. Find the solution to the differential equation that models the mixing process.

Question 57

Solve the initial value problem.

Question 58

A 200 gal tank is half full of distilled water. At time = 0, a solution containing 1 lb/gal of concentrate enters the tank at the rate of 4 gal/min, and the well-stirred mixture is withdrawn at the rate of 2 gal/min. When the tank
Is full, how many pounds of concentrate will it contain?

A) 200 pounds
B) 150 pounds
C) 120 pounds
D) 100 pounds

Question 59

Solve the problem.
dy/dt = ky + f(t) is a population model where y is the population at time t and f(t) is some function to describe the net effect on the population. Assume k = .02 and y = 10,000 when t = 0. Solve the differential equation of y
When f(t) = 20t.

A) y = 1000t + 50,000 + 60,000e-.02t
B) y = -1000t - 50,000 + 60,000e.02t
C) y = -1000t - 50,000 + 60,000e-.02t
D) y = 1000t - 50,000 + 60,000e-.02t

Question 60

Determine which of the following equations is correct.

Question 61

A 59-kg skateboarder on a 1-kg board starts coasting on level ground at 10 m/sec. Let k = 3.2 kg/sec. How long will it take the skater's speed to drop to 2 m/sec?

A) -30.18 sec
B) 29.67 sec
C) 30.18 sec
D) 0.50 sec

Question 62

Identify equilibrium values and determine which are stable and which are unstable.

A) y = 4 is a stable equilibrium value and y = -4 is an unstable equilibrium.
B) y = -4 and y = 5 are stable equilibrium values.
C) y = -4 is a stable equilibrium value and y = 4 is an unstable equilibrium.
D) There are no equilibrium values.

Question 63

Show that the curves are orthogonal.

Question 64

A local pond can only hold up to 43 geese. Eight geese are introduced into the pond. Assume that the rate of growth of the population is where t is time in weeks.
How long will it take for the goose population to be 24?

A) 35.07 weeks
B) 58.74 weeks
C) 13.84 weeks
D) 26.50 weeks

Question 65

Solve the initial value problem

Question 66

Find the orthogonal trajectories of the family of curves. Sketch several members of each family.
y = -mx

Question 67

Question 68

Identify equilibrium values and determine which are stable and which are unstable.

A) y = 2 is an unstable equilibrium value.
B) y = 0 is a stable equilibrium value.
C) y = 0 is an unstable equilibrium value.
D) There are no equilibrium values.

Question 69

Show that the curves are orthogonal.

Question 70

Identify equilibrium values and determine which are stable and which are unstable.

A) y = 5, y = 1 and y = 4 are unstable equilibria.
B) y = 1 is a stable equilibrium value and y = 3 and y = 4 are unstable equilibria.
C) y = 4 is a stable equilibrium value and y = 3 and y = 1 are unstable equilibria.
D) y = 3 is a stable equilibrium value and y = 1 and y = 4 are unstable equilibria.

Question 71

A local pond can only hold up to 56 geese. Five geese are introduced into the pond. Assume that the rate of growth of the population is where t is time in weeks.
Find a formula for the goose population in terms of t.

Question 72

Find the orthogonal trajectories of the family of curves. Sketch several members of each family.

Question 73

A 53-kg skateboarder on a 1-kg board starts coasting on level ground at 10 m/sec. Let k = 3.2 kg/sec. About how far will the skater coast before reaching a complete stop?

A) 16.96 m
B) 168.75 m
C) 1696.00 m
D) 165.62 m

Question 74

Identify equilibrium values and determine which are stable and which are unstable.

A) y = 3 is a stable equilibrium value and y = 0 is an unstable equilibrium.
B) y = 0 is a stable equilibrium value and y = 3 is an unstable equilibrium.
C) y = 0 and y = 3 are unstable equilibrium values.
D) There are no equilibrium values.

Question 75

Identify equilibrium values and determine which are stable and which are unstable.