Free Printable Math021 A6

1.

3.The order and degree of the differential equation : $\sqrt[]{\frac{\text{d}^2x}{\text{d}y^2}}=\sqrt[]{\frac{\text{d}x}{\text{d}y}+5}$

a)

2 and 3

b)

3 and 2

c)

2 and 1

d)

1 and 1

2.

6.The Solution of y''-6y'+9y=0 is

a)

(c₁+c₂x)e^3x

b)

(c₁+c₂x)e^-3x

c)

c₁e^3x+c₂e^-3x

d)

None

3.

8.The number of arbitrary constants in the general solution of differential equation of second order is ……

a)

1

b)

0

c)

3

d)

2

4.

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

5.

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

6.

$\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)

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

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 $\frac{d^2y}{dx^2}+2\frac{\text{d}y}{\text{d}x}+y=0$ is

a)

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

b)

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

c)

$c_1e^x+c_2e^x$

d)

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

9.

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)

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

10.

Determine the order of the following equation $5\left(\frac{\text{d}^4x}{\text{d}y^4}\right)^3+7\left(\frac{\text{d}x}{\text{d}y}\right)^{10}+y=x$

a)

10

b)

7

c)

12

d)

4

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.

$\frac{\text{d}^2x}{\text{d}y^2}-y=\cot x$
The above DE can be solved using the undetermined coefficient meThod.

a)

TRUE

b)

FALSE

13.

Given $\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}+3y=2e^{-x}.$

The correct $y_p$ is

a)

$Ce^{-x}$

b)

$C\cos x+D\sin x$

c)

$Ce^x$

d)

$Cxe^{-x}$

14.

The initial guess for $f\left(x\right)-4\cos3x+2x^2$

a)

$y_p=\left(C\cos3x+Fx^2\right)$

b)

$y_p=\left(C\cos3x+D\sin3x+Fx^2+Gx+H\right)$

c)

$y_p=\left(C\cos3x+D\sin3x+Fx^2\right)$

d)

$y_p=\left(C\cos3x-D\sin3x+Fx^2+G\right)$

15.

$\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}-6y=0$

Which of the following options are TRUE about the above DE?

a)

The roots of the auxiliary equations are two complex roots.

b)

The auxiliary equation has two different roots.

c)

The auxiliary equation has two equal roots.

d)

The equation is homogeneous.

16.

The general solution of the DE
$\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}-5y=0$ is

a)

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

b)

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

c)

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

d)

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

17.

The roots of the auxiliary equation
$\frac{\text{d}x}{\text{d}y}+16y=0$ is

a)

$y=A\cos16x+B\sin16x$

b)

$y=A+Be^{-16x}$

c)

$y=A\cos4x+B\sin4x$

d)

$y=Ae^{4x}+Be^{-4x}$

18.

$\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)

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

19.

What is the general solution to the DE $\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0$ ?

a)

$y=Ce^{-x}+De^{8x}$

b)

$y=Ce^x+De^{-8x}$

c)

$y=Ce^x+De^{7x}$

d)

$y=Ce^{-x}+De^{7x}$

20.

Determine the general solution of $y"-2y'+y=0$

a)

$y=C_1e^x+C_2xe^x$

b)

$y=C_1e^x+C_2e^x$

c)

$y=e^x\left(C_1\cos x+C_2\sin x\right)$

d)

$y=C_1e^x+C_2xe^{-x}$

21.

Determine the general solution of $y"+5y'+6y=0$

a)

$y=C_1e^{-3x}+C_2xe^{-2x}$

b)

$y=C_1e^{-3x}+C_2e^{-2x}$

c)

$y=e^{-3x}\left(C_1\cos2x+C_2\sin2x\right)$

d)

$y=C_1e^{3x}+C_2e^{-2x}$

22.

Determine the general solution of $y"-2y'+5y=0$

a)

$y=C_1e^x+C_2xe^{2x}$

b)

$y=C_1e^x+C_2e^{2x}$

c)

$y=C_1e^x\cos2x+C_2e^x\sin2x$

d)

$y=C_1e^{2x}\cos x+C_2e^{2x}\sin x$

23.

Determine the general solution of $9y"+6y'+y=0$

a)

$y=C_1e^{-\frac{x}{3}}+C_2xe^{-\frac{x}{3}}$

b)

$y=C_1e^{-\frac{x}{3}}+C_2e^{-\frac{x}{3}}$

c)

$y=e^{-\frac{x}{3}}\left(C_1\cos x+C_2\sin x\right)$

d)

$y=e^x\left(C_1\cos\frac{x}{3}+C_2\sin\frac{x}{3}\right)$

24.

Determine the general solution of $4y"-4y'+y=0$

a)

$y=C_1e^{\frac{x}{2}}+C_2xe^{\frac{x}{2}}$

b)

$y=C_1e^{\frac{x}{2}}+C_2xe^{-\frac{x}{2}}$

c)

$y=e^{-\frac{x}{3}}\left(C_1\cos x+C_2\sin x\right)$

d)

$y=C_1e^{\frac{x}{2}}+C_2e^{\frac{x}{2}}$

25.

Determine the general solution of $4y"+12y'+9y=0$

a)

$y=C_1e^{-\frac{3}{2}x}+C_2xe^{-\frac{3}{2}x}$

b)

$y=C_1e^{-\frac{3}{2}}+C_2xe^{-\frac{3}{2}}$

c)

$y=e^{-\frac{3}{2}x}\left(C_1\cos\frac{3}{2}x+C_2\sin\frac{3}{2}x\right)$

d)

$C_1e^{-\frac{3}{2}x}+C_2e^{-\frac{3}{2}x}$

26.

Determine the general solution of $25y"-20y'+4y=0$

a)

$y=C_1e^{\frac{2}{5}x}+C_2e^{\frac{2}{5}x}$

b)

$y=C_1e^{\frac{2}{5}x}+C_2xe^{-\frac{2}{5}x}$

c)

$y=e^{\frac{2}{5}x}\left(C_1\cos x+C_2\sin x\right)$

d)

$C_1e^{\frac{2}{5}x}+C_2xe^{\frac{2}{5}x}$

27.

Determine the general solution of $y"-6y'+9y=0$

a)

$y=C_1e^{3x}+C_2e^{3x}$

b)

$y=C_1e^x+C_2xe^{3x}$

c)

$y=e^{3x}\left(C_1\cos3x+C_2\sin3x\right)$

d)

$C_1e^{3x}+C_2xe^{3x}$

28.

Determine the general solution of $y"+2y'-8y=0$

a)

$y=C_1e^{-4x}+C_2xe^{2x}$

b)

$y=C_1e^{-4x}+C_2e^{2x}$

c)

$y=e^{4x}\left(C_1\cos2x+C_2\sin2x\right)$

d)

$y=e^{2x}\left(C_1\cos4x+C_2\sin4x\right)$

29.

Determine the general solution of $9y"+9y'-4y=0$

a)

$y=C_1e^{-\frac{1}{3}x}+C_2e^{\frac{4}{3}x}$

b)

$y=C_1e^{\frac{1}{3}x}+C_2e^{-\frac{4}{3}x}$

c)

$y=e^{\frac{1}{3}x}\left(C_1\cos\frac{4}{3}x+C_2\sin\frac{4}{3}x\right)$

d)

$y=C_1e^{\frac{1}{3}x}+C_2xe^{-\frac{4}{3}x}$

30.

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

31.

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)

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

32.

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)

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

33.

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

34.

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

a)

Separable.

b)

Non Separable

35.

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

36.

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)

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

37.

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)

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

38.

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)

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

39.

$\frac{d^2y}{dx^2}+y=e^xx$ , 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)

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

40.

$Solution\ of\ \ xdx+ydz+zdy=0$ , 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)

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

Math021 A6

Total questions: 40

Worksheet time: 35mins

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