Chapter 11 Practice Test Flashcards Preview

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Flashcards in Chapter 11 Practice Test Deck (12):
1

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

yeydy=1x2dx

2

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

32x2+2x=13y3−y+C

3

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

true

4

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

y=12x2+3

5

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

y = x 3 + x 2

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.

y(2)≈6.5625

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.

480

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.

13.6 hours

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?

$1,454.99

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.

5.4 g

11

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

y=12e2x+C

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?

dPdt=0.3P

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