Differential Equations — Course Quiz

The order of

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

is

A

3

B

1

C

5

D

2

The degree of

y'' + \sin(y') = 0

is

A

2

B

0

C

1

D not defined

Eliminating

m

from

y = mx

gives which differential equation?

A

\displaystyle y = x\dfrac{dy}{dx}

B

\displaystyle \dfrac{dy}{dx} = m

C

\displaystyle \dfrac{d^2y}{dx^2} = 0

only

D

\displaystyle x = y\dfrac{dy}{dx}

Solve

\displaystyle \dfrac{dy}{dx} = \dfrac{y}{x}

with

y(2) = 6

.

A

y = x + 4

B

y = 6x

C

\displaystyle y = \tfrac{3}{2}x^2

D

y = 3x

Solve

\displaystyle \dfrac{dy}{dx} = 2y

with

y(0) = 5

.

A

y = e^{2x} + 4

B

y = 2e^{5x}

C

y = 5e^{x^2}

D

y = 5e^{2x}

A substance decays at a rate proportional to the amount present, and half of it disappears in

20

years. How long until only

\displaystyle \tfrac{1}{4}

remains?

A

80

years

B

40

years

C

30

years

D

60

years

The integrating factor of

\displaystyle \dfrac{dy}{dx} + 2xy = x

is

A

e^{x^2}

B

x^2

C

e^{-x^2}

D

e^{2x}

Solve

\displaystyle \dfrac{dy}{dx} + y = 1

with

y(0) = 0

.

A

y = 1 + e^{-x}

B

y = 1 - e^{x}

C

y = 1 - e^{-x}

D

y = e^{x} - 1

Which differential equation is homogeneous?

A

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

B

\displaystyle \dfrac{dy}{dx} = \dfrac{x + 1}{y}

C

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

D

\displaystyle \dfrac{dy}{dx} = e^{x}y

The general solution of

\displaystyle \dfrac{dy}{dx} + \dfrac{y}{x} = 1

(

x > 0

) is

A

\displaystyle \dfrac{y}{x} = \log x + C

B

\displaystyle xy = \dfrac{x^2}{2} + C

C

xy = x + C

D

\displaystyle y = \dfrac{x^2}{2} + C

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Differential Equations — Course Quiz

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