Free Printable DIFFERENTIAL EQUATION CLASS 12

1.

dy/dx = 2x/e^2y find the general solution

a)

y = ln (2x/2 + C)

2

b)

y = ln(2x/2)+c

c)

y = e^2x+c

d)

y = mx+b

2.

Dy/dx= tanx+15x2+e^x+1/x

a)

y= -ln|sinx| + 5x³ + e^x + ln|x| + c

b)

y= secxtanx + 5x³ + e^x + ln|x| + c

c)

y= -ln|cosx| + 5x³ + e^x + ln|x| + c

d)

y= sec²(x) + 5x³ + e^x + ln|x| + c

3.

Find the particular solution for y if dy/dx = 2x√y and y = 4 when x = 3.

a)

2√y = x² + C

b)

y = (x² + 25)²/4

c)

y = (x²/2-5/2)^1/2

d)

y = x⁴/4

4.

dy/dx = 4x/y. Suppose y(0)=1
The particular solution is

a)

B

b)

C

c)

D

d)

E

5.

Determine the order and degree.

a)

1, 2

b)

2, 2

c)

1, 1

d)

2, 1

6.

What is the order and degree of the differential equation?

a)

1, 2

b)

2, 1

c)

3, 2

d)

2, 3

7.

What is the order of the D.E. (d²y/dx²)²+ y = 0

a)

1

b)

2

c)

3

d)

0

8.

Integrating factor of the differential equation $x\frac{\text{d}y}{\text{d}x}-y=\sin x$

a)

$-\frac{1}{x}$

b)

$\frac{1}{x}$

c)

$\ln\left|x\right|$

d)

$\frac{1}{x^2}$

9.

The solution of linear differential equation $x\frac{\text{d}y}{\text{d}x}+2y=x^2$

a)

$y=\frac{x^2+c}{4x^2}$

b)

$y=\frac{x^2}{4}+c$

c)

$y=\frac{x^4+c}{x^2}$

d)

$y=\frac{x^4+c}{4x^2}$

10.

By separation of variables, solve the resulting equations $\int\ \frac{v}{v+1}dv=\int_{ }^{ }\ \frac{1}{y}dy\text{}$

a)

$\frac{x}{y}-\ln\left|\frac{x}{y}+1\right|=\ln y+C$

b)

$\frac{x}{y}+\ln\left|\frac{x}{y}+1\right|=\ln y+C$

c)

$\frac{x}{y}+\frac{x^2}{2y^2}=\ln y+C$

d)

$\frac{x}{y}-\frac{x^2}{2y^2}=\ln y+C$

11.

Solve the given differential equations by separable variable method $\frac{\text{d}v}{\text{d}t}=\frac{3+v^2}{v}$

a)

$v=\ln\left|3+v^2\right|+C$

b)

$v^2=e^{2t+2c}-3$

c)

$v=Ae^{2t}+3,\ \ \ \ \ A=e^{2c}$

d)

$v^2=Ae^{2t}+3,\ \ \ \ \ \ A=C$

12.

Solve the given differential equations by separable variable method $\frac{\text{d}y}{\text{d}x}=e^{-y}\left(2x-4\right),\ \ \ \ \ y\left(5\right)=0$

a)

$y=\ln\left|x^2-4x-4\right|$

b)

$y=x^2-4x-4$

c)

$y=4e^{2t}+4\ \ \ \ \ A=e^{2c}$

d)

$y^2=4e^{2x}+2,\ \ \ \ \ \ A=C$

13.

The solution of linear differential equation $\frac{\text{d}y}{\text{d}x}+y=e^x$

a)

$y=\frac{e^2+c}{4x^2}$

b)

$y=\frac{ex^2}{4}+c$

c)

$y=\frac{e^{4x}+c}{x^2}$

d)

$y=\frac{e^x}{2}+Ce^{-x}$

14.

The degree of the differential equation

\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{1}{2}}=\frac{d^2y}{dx^2}\ is:

a)

4

b)

$\frac{3}{2}$

c)

not defined

d)

2

15.

What is the integrating factor for the differential equation: $\frac{1}{x}\frac{\text{d}x}{\text{d}y}-\frac{1}{1+x^2}y=x^3$

a)

$\ln\left(x^2\right)$

b)

$-\frac{1}{x^2}$

c)

$-\frac{1}{\sqrt{x}}$

d)

$\frac{1}{\sqrt{x}}$

DIFFERENTIAL EQUATION CLASS 12

Total questions: 15

Worksheet time: 1hrs 15mins

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