Free Printable Higher order linear differential equations

1.

The complete solution(or complete integral ) 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 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)

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

3.

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)

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

4.

Number of arbitrary constant in the general solution of a differential equation of degree 3 and order 4 is

a)

3

b)

4

c)

0

d)

4³

5.

$\frac{\text{d}^2x}{\text{d}y^2}+6\frac{\text{d}x}{\text{d}y}-5y=0\$

The general solution to the DE is,

a)

$y=Ae^x+Be^{5x}$

b)

$y=Ae^{-x}+Be^{-5x}$

c)

$y=Ae^{\left(-3+\sqrt{14}\right)x}+Be^{\left(-3-\sqrt{14}\right)x}$

d)

$y=A\cos\left(-3+\sqrt{14}\right)x+B\sin\left(-3-\sqrt{14}\right)x$

6.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$

a)

Separable.

b)

Non Separable

7.

Differential equation of the curve y= Acos2x+B sin2x , where A & B are constant is

a)

y^"+4y=0

b)

y^"-4y=0

c)

y^" -4y^'=0

d)

y^"+4y^'=0

8.

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)

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

9.

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)

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

10.

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)

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

11.

$x^2\frac{\text{d}^2x}{\text{d}y^2}-5y=x+1$ is a non homogeneous second order differential equations with constant coefficients.

a)

TRUE

b)

FALSE

12.

$\frac{d^2y}{dx^2}+ay=\operatorname{cosec}x\$ can be solved by finding

a)

C.F and P.I

b)

singular solution

c)

General solution by variation of parameter method

d)

total differential equation steps

13.

$\frac{d^2y}{dx^2}+y=e^xx$ , Particular integral is given by

a)

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

b)

$\frac{e^x\left(x-1\right)}{2}$

c)

$\frac{e^xx}{3}$

d)

$\frac{e^x\left(x+1\right)}{2}$

14.

$Solution\ of\ \ xdx+ydz+zdy=0$ , Particular integral is given by

a)

$\frac{\text{}x^2}{\text{2}}+y-z$

b)

$\frac{x^2}{2}+xy$

c)

$\frac{x^2}{2}^{ }+yz$

d)

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

Higher order linear differential equations

Total questions: 14

Worksheet time: 1hrs 10mins

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