Free Printable EEE -Differential Equations types

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.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

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

c)

$y=e^x+C$

d)

$0=e^x+C$

3.

Of the following, which is a solution to the differential equation, select all that apply:
$y''-6y'+8y=0$

a)

$y=2\sin\left(4x\right)$

b)

$y=3e^{2x}$

c)

$y=Ce^{4x},\$ where C is a constant

4.

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)

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

5.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=3y$

a)

$y=Ce^{3x}$

b)

$y=3x+C$

c)

$\frac{y^2}{2}=3x+C$

d)

$\ln y=x+C$

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 a differential equation?

a)

the highest power of y

b)

The highest power of x

c)

the highest order of the derivative

d)

the coefficient of y

8.

Example of homogenous equation

a)

m²+2m+3

b)

m²+3m+2

c)

(m²+5m+6)y=0

d)

m²+5m+6=5

9.

Identify the roots of the equation m²-8m+16=0 is

a)

Real and distinct

b)

imaginary

c)

real and equal

d)

no roots

10.

If the roots are imaginary the complementary function is

a)

Y=Aeᵐ1ˣ+Beᵐ2ˣ

b)

Y=eᵅˣ(Acosβx +Bsinβx)

c)

.Y=(Ax+B)eᵐˣ

d)

None of the above

11.

The auxiliary equation of (D²+5D+6)y=0 is

a)

a.m²+2m+3

b)

m²+3m+2

c)

(m²+5m+6)y=0

d)

m²+5m+6=0

12.

Find the roots of the auxiliary equation m³-6m²+11m-6=0

a)

1 2 3

b)

2 3

c)

4 2

d)

0 2 3

13.

In the general equation (a d²/dx² + b d/dx + c)y =V , d²/dx² denotes

a)

D

b)

D²

c)

m

d)

m²

14.

Find the particular integral (D²+8D+16)y=e⁻²ˣ

a)

(Ax+B)e⁻²ˣ+e⁻⁴ˣ/4

b)

(Ax+B)e⁻⁴ˣ+e⁻ˣ/2

c)

(Ax+B)+e⁻⁴ˣ+e⁻²ˣ/4

d)

(Ax+B)e⁻⁴ˣ+e⁻²ˣ/4

15.

Solve (D²-5D+6)y=3e⁵ˣ

a)

Y=Ae²ˣ+Be³ˣ+e⁵ˣ/6

b)

Y=Ae⁻²ˣ+Be⁻³ˣ+e⁵ˣ/2

c)

Y=Ae²ˣ+Be³ˣ+e⁵ˣ/2

d)

Y=(Ax+B)e²ˣ+e¹⁵ˣ/2

EEE -Differential Equations types

Total questions: 15

Worksheet time: 10mins

Similar Resources on Wayground