Chapter 11 Practice Test

Question 1

Separate the variables of the equation: x^2ydydx=e^y

Answer 1

yeydy=1x2dx

Question 2

Solve the following differential equation for the general solution: dy/dx=3x+2y2−1

Answer 2

32x2+2x=13y3−y+C

Question 3

Evaluate the following as true of false.The equation xy+xxy−y=dydx is a separable differential equation.

Answer 3

true

Question 4

Find the particular solution to dy/dx=x if y(2)=5.

Answer 4

y=12x2+3

Question 5

Which of the following is not a solution of d2ydx2=6x?

Answer 5

y = x 3 + x 2

Question 6

Use Euler’s method with step size 0.5 to compute the approximate y-value y (2) of the solution of the initial-value problem y′ = xy, y (0) = 2.

Answer 6

y(2)≈6.5625

Question 7

Use Euler’s method with step size 0.5 to compute the approximate y-value y (2) of the solution of the initial-value problem y′ = xy, y (0) = 2.

Answer 7

480

Question 8

The population of a colony of 300 bacteria grows exponentially. After 2 hours, the population reaches 500. How much time will it take for the population to reach 9,600? Give the answer to the nearest tenth of an hour.

Answer 8

13.6 hours

Question 9

One thousand dollars is invested at 5% continuous annual interest. This means the value of the investment will grow exponentially, with k equaling the decimal rate of interest. What will the value of the investment be after 7 1/2 years?

Answer 9

$1,454.99

Question 10

The half-life of iodine-126 (I 126 ) is 13 days. Of an original sample of 1,000.0 grams, how may grams of I 126 will remain after 98 days? Give the answer to the nearest tenth of a gram.

Answer 10

5.4 g

Question 11

Solve the following differential equation for the general solution: dy/dx=e2x.

Answer 11

y=12e2x+C

Question 12

Suppose the fish population in a local lake increases at a yearly rate of 0.3 times the population at each moment. Which of the following differential equations describes the rate of change of the fish population in the lake?

Answer 12

dPdt=0.3P