Free Printable Differential Equations

1.

Given the differential equation dP/dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

a)

A) P=Ce^5t

B) P= 5e^418t

b)

A) P=Ce^5t

B) P= 418e^5t

c)

A) P=Ce^t

B) P= 418e^t

d)

A) P=Ce^10t

B) P= 418e^10t

2.

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

3.

dy/dx= x √y

Find the general solution

a)

√y = ln|4x| + c

b)

√y = (x)^-1 + c

c)

2y^1/2= ln|x| + c

d)

1/2y^1/2= ln|x| + c

4.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

5.

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

6.

it is number of the highest degree in a differential equation

a)

variable

b)

degree

c)

order

d)

derivative

7.

The power of the differential equation's highest derivative, after the equation has been made rational and integral in all of its derivatives

a)

order

b)

degree

c)

exponent

d)

variable

8.

in $\frac{\text{d}x}{\text{d}y}$ , which is the dependent variable?

a)

x

b)

y

c)

d

d)

secret

9.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=y^2+xy^2$

a)

Separable.

b)

Non Separable.

10.

Differential equation of the curve y=Acosx-Bsinx, where A and B are arbitrary constant is

a)

y^"+xy=0

b)

y^"-y=0

c)

y^"+y=0

d)

y^"+x=0

11.

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)

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

12.

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)

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

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.

Order and degree of the D.E. y^''+logy^'''-xy+(y''')³=0

a)

3,1

b)

2,3

c)

order -3,degree not defined

d)

3,3

15.

The degree of a differential equation is define by a

a)

Positive real number

b)

Positive rational number

c)

Positive integer

d)

All the above

16.

Solution of a linear differential equation of first order can be obtain by

a)

multiplying on both the sides by its integrating factor.

b)

adding on both the sides by integrating factor.

c)

subtracting integrating factor from both sides

d)

None of the above

17.

Solve the differential equation

sec²xtanydx+sec²ytanxdy=0

a)

-sinx tany=c

b)

sinx tany=c

c)

tanx tany=c

d)

-tanx tany=c

18.

Solve the differential equation at x=1,y=0

dy/dx =1+x+y+xy

a)

log|1-y| =x+x²/2 -3/2

b)

log|1+y| =2x+x²/2 -3/2

c)

log|1+y| =x+x²/2 -3/2

d)

log|1+y| =x+x²/2 +3/2

19.

Solve the differential equation

(x-y)dy-(x+y)dx=0

a)

tan^-1(y/x)+(1/2)log|x²+y²|+c

b)

-tan^-1(y/x)-(1/2)log|x²+y²|+c

c)

tan^-1(y/x)-(1/2)log|x²+y²|+c

d)

tan^-1(y/x)-(1/3)log|x²+y²|+c

20.

Solve the differential equation

xdy/dx =y-xtan(y/x)

a)

sin(y/x) =c/x

b)

-sin(y/x) =c/x

c)

cos(y/x) =c/x

d)

tan(y/x) =c/x

21.

Which of the following differential equation is a homogeneous equation of degree 2?

a)

$\frac{\text{d}y}{\text{d}x}=2xy$

b)

$y\frac{\text{d}y}{\text{d}x}=2x$

c)

$\frac{\text{d}y}{\text{d}x}=\frac{3xy+y^2}{xy}$

d)

$xy\frac{\text{d}y}{\text{d}x}=y^2-1$

22.

Which of the following differential equations can be classified as separable and exact?

a)

$y^3dx+3xy^2dy=0$

b)

$\frac{\text{d}y}{\text{d}x}=\frac{x+y}{x}$

c)

$\frac{\text{d}y}{\text{d}x}=3\left(y+5\right)x$

d)

$\left(x^2+1\right)dy+\left(xy+x\right)dx=0$

23.

The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially?

a)

1

b)

About 16

c)

About 40

d)

About 53

24.

Integrate $\int_{ }^{ }\left(\frac{1-\sin x}{\cos^2x}\right)dx$

a)

$\tan x-\sec x+c$

b)

$\tan x+\sec x+c$

c)

$\cot x-\operatorname{cosec}x+c$

d)

$\cot x+\operatorname{cosec}x+c$

25.

Evaluate the indefinite integral using integration by parts.
$\int3x\ e^{2x}\ dx\$

a)

$-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$

b)

$\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$

c)

$xe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C$

d)

$-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$

Differential Equations

Total questions: 25

Worksheet time: 42mins

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