Free Printable Higher Order Linear Differential Equations

1.

The complete solution of Linear Differential equations involves

a)

complete function + particular integral

b)

complementary function + particular integral

c)

complementary function + definite integral

d)

complete function + indefinite integral

2.

The complementary function of the equation $\frac{d^2y}{dx^2}+2\frac{\text{d}y}{\text{d}x}+y=0$ is

a)

$c_1e^x+c_2e^{-x}$

b)

$c_1e^{-x}+c_2e^{-x}$

c)

$c_1e^x+c_2e^x$

d)

$\left(c_1+c_2x\right)e^{-x}$

3.

The complementary function of the equation $2\frac{d^2y}{dt^2}+5\frac{\text{d}y}{\text{d}t}-12y=0$ is

a)

$c_1e^{\frac{3}{2}x}+c_2e^{-4x}$

b)

$c_1e^{\frac{3}{2}t}+c_2e^{-4t}$

c)

$c_1e^{-\frac{3}{2}x}+c_2e^{4x}$

d)

$c_1e^{-\frac{3}{2}t}+c_2e^{4t}$

4.

The complementary function of the equation $\frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}=0$ is

a)

$\left(c_1+c_2x\right)+c_3e^x$

b)

$\left(c_1+c_2x\right)+c_3e^{-x}$

c)

$\left(c_1+c_2\right)+c_3e^x$

d)

$\left(c_1+c_2x\right)+c_3e^{-2x}$

5.

The particular integral of the equation $\left(D-1\right)y=e^{3x}$ is

a)

$\frac{e^{3x}}{2}$

b)

$\frac{e^{-3x}}{2}$

c)

$\frac{e^{3x}}{4}$

d)

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

6.

The particular integral of the equation $\left(D^3-1\right)y=\left(e^x+1\right)^2$ is

a)

$\frac{e^{-2x}}{7}+\frac{2x}{3}-1$

b)

$\frac{e^{3x}}{7}+\frac{2x}{3}-1$

c)

$\frac{e^{2x}}{7}+\frac{5x}{3}-1$

d)

$\frac{e^{2x}}{7}+\frac{2x}{3}-1$

7.

The C.F. of the equation $\left(D^2-9\right)y=e^{-3x}+1+e^{3x}$ is

a)

$c_1e^{-3x}+c_2e^{-x}$

b)

$c_1e^{3x}+c_2e^{3x}$

c)

$c_1e^{3x}+c_2e^{-x}$

d)

$c_1e^{3x}+c_2e^{-3x}$

8.

The C.F. of the equation $\frac{d^2y}{dx^2}+\frac{3dy}{dx}+2y=e^{-x}$ is

a)

$c_1e^{-x}+c_2e^{-2x}$

b)

$c_1e^x+c_2e^{2x}$

c)

$c_1e^{-2x}+c_2e^{-2x}$

d)

$c_1e^{3x}+c_2e^{2x}$

9.

The P.I. of the equation $\left(D^3+D\right)y=\cos x\$ is

a)

$-\frac{x\cos x}{2}$

b)

$\frac{x\cos x}{2}$

c)

$-\frac{\cos x}{2}$

d)

$-\frac{x\cos x}{5}$

10.

The C.F. of the equation $\left(D^2-4\right)y=\sin^2x$ is

a)

$c_1e^{-x}+c_2e^{2x}$

b)

$c_1e^x+c_2e^{-2x}$

c)

$c_1e^x+c_2e^{2x}$

d)

$c_1e^{4x}+c_2e^{2x}$

Higher Order Linear Differential Equations

Total questions: 10

Worksheet time: 10mins

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