Free Printable Differential Equation Test

1.

Degree of $\left[1+\left(\frac{\text{d}y}{\text{d}x}\right)^2\right]^3=\left(\frac{\text{d}^2y}{\text{d}x^2}\right)^2$ is ______

a)

6

b)

2

c)

3

d)

4

2.

The order of $x\frac{\text{d}^2y}{\text{d}x^2}-\left(2x-1\right)\frac{\text{d}y}{\text{d}x}+\left(x-1\right)y=e^x$ is ______

a)

2

b)

1

c)

0

d)

Not defined

3.

The complimentary solution of $\left(D^3-D^2-4D+4\right)y=0$

a)

$y=c_1+c_2e^{2x}+c_3e^{-2x}$

b)

$y=c_1e^x+c_2e^{2x}+c_3e^{-4x}$

c)

$y=c_1e^{3x}+c_2e^{4x}+c_3e^{-2x}$

d)

$y=c_1e^x+c_2e^{2x}+c_3e^{-2x}$

4.

Find the general solution of $\frac{\text{d}y}{\text{d}x}=e^{\left(x+y\right)}$

a)

$e^y=e^x+c$

b)

$e^{-y}=e^x+c$

c)

$-e^{-y}=e^x+c$

d)

$-e^{-y}=e^{-x}+c$

5.

Find the Integrating Factor of $\frac{\text{d}u}{\text{d}x}-\frac{u}{x}=\frac{1}{x^2}$

a)

$x$

b)

$\frac{1}{x}$

c)

$e^x$

d)

$e^{-x}$

6.

Find the particular Integral of $\left(D^2+D+1\right)y=\sin x$

a)

sinx

b)

$\cos\ x$

c)

$-\cos\ x$

d)

-x cosx

7.

The solution of clairaut's equation $y=xp+\frac{2}{p}$ where $p=\frac{\text{d}y}{\text{d}x}$ is______

a)

$y=x+\frac{2}{c}$

b)

$y=xc+\frac{2}{c}$

c)

$y=xc+2c$

d)

None

8.

The Differential equation $x\left(1+y^2\right)dx+y\left(1+x^2\right)dy=0$ is

a)

Homogeneous Equation

b)

Linear Equation

c)

Bernouli Equation

d)

Exact Equation

9.

Form a differential equation whose solution is $y=Ae^{2x}+Be^{-2x}$ where A ,B are arbitary constants

a)

$\frac{\text{d}^2y}{\text{d}x^2}+4\frac{\text{d}y}{\text{d}x}-4y=0$

b)

$\frac{\text{d}^2y}{\text{d}x^2}-4\frac{\text{d}y}{\text{d}x}=0$

c)

$\frac{\text{d}^2y}{\text{d}x^2}+\frac{\text{d}y}{\text{d}x}-4y=0$

d)

$\frac{\text{d}^2y}{\text{d}x^2}-4y=0$

10.

The Integrating Factor of Homogeneous equation Mdx+Ndy=0 is___

a)

$\frac{1}{Mx+Ny}$

b)

$\frac{1}{Mx-Ny}$

c)

$\frac{1}{M}\left(\frac{1}{Mx+Ny}\right)$

d)

$\frac{1}{N}\left(\frac{1}{Mx+Ny}\right)$

Differential Equation Test

Total questions: 10

Worksheet time: 6mins

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