Differential Equations and Separable Variables — Quiz

The order and degree of

\displaystyle \left(\dfrac{d^2y}{dx^2}\right)^2 + \left(\dfrac{dy}{dx}\right)^3 + y = 0

are

A order

2

, degree

2

B order

2

, degree

3

C order

1

, degree

3

D order

3

, degree

2

y = Ae^{2x} + Be^{-2x}

is a solution of

A

y'' = 4y

B

y'' = 2y

C

y'' = -4y

D

y' = 4y

How many arbitrary constants does the general solution of a third-order differential equation contain?

A

0

B

3

C

1

D

2

Solve

\displaystyle \dfrac{dy}{dx} = 3x^2y

with

y(0) = 2

.

A

y = 2e^{3x^2}

B

y = 2e^{x^3}

C

y = e^{x^3} + 1

D

y = x^3 + 2

A population grows at a rate proportional to its size and doubles in

5

years. How many times its original size is it after

15

years?

A

3

B

9

C

8

D

6

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