Free Printable EM-1 QUIZ 1

1.

$Find\ Complementary\ function\ of\ \left(D^3-6D^2+11D-6\right)y=0$

a)

$Ae^x+Be^{2x}+Ce^{3x}$

b)

$Ae^{2x}+Be^{3x}+Ce^{0x}$

c)

$\left(Ax+B\right)e^{3x}$

d)

$Ae^{2x}+\left(Bx+C\right)e^x$

2.

$Find\ CF\ of\ \left(D^3+1\right)y=0\ Given\ y\left(o\right)=1,y\left(\frac{\pi}{2}\right)=0$

a)

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

b)

$y\left(x\right)=\cos x$

c)

$y\left(x\right)=\sin x+\cos x$

d)

$y\left(x\right)=\cos x+\sin x$

3.

$Find\ Particular\ integral\ \ of\ \left(4D^2-4D+1\right)y=4$

a)

12

b)

16

c)

4

d)

8

4.

$Find\ the\ PI\ of\ \left(D^2-1\right)y\ =\ \left(e^x+1\right)^2$

a)

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

b)

$e^{2x}-1+xe^x$

c)

$e^x+xe^{2x}-1$

d)

$e^x\left(x+1\right)$

5.

$Find\ the\ PI\ of\ \left(D^2+3D+2\right)y=\sin3x$

a)

$-\frac{1}{130}\left(7\sin3x+9\cos3x\right)$

b)

$\frac{1}{130}\left(9\sin3x+7\cos3x\right)$

c)

$\left(7\sin3x+9\cos3x\right)$

d)

$\left(\sin3x+\cos3x\right)$

6.

$Find\ the\ PI\ of\ \left(D^2+2D+2\right)y=\cos2x$

a)

$-\frac{1}{10}\cos2x+\frac{1}{5}\sin2x$

b)

$\frac{1}{5}\cos2x+\frac{1}{10}\sin2x$

c)

$\cos2x+\sin2x$

d)

$-\frac{1}{5}cs2x+\sin2x$

7.

$Find\ the\ PI\ of\ \left(D^2-D\right)y=x$

a)

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

b)

$x^2+1$

c)

$x+1$

d)

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

8.

$Find\ the\ PI\ of\ \left(D^3-3D^2-6D+8\right)y=x$

a)

$\frac{1}{8}\left(x+\frac{3}{4}\right)$

b)

$\left(x+\frac{3}{4}\right)$

c)

$\frac{1}{3}\left(x+\frac{4}{3}\right)$

d)

$\frac{1}{8}\left(x+\frac{4}{3}\right)$

9.

$Find\ the\ PI\ of\ \left(D^2+2D+1\right)y=e^{-x}x^2$

a)

$\frac{e^xx^4}{12}$

b)

$\frac{e^{-x}x^4}{12}$

c)

$e^{-x}x^4$

d)

$e^xx^4$

10.

$Find\ the\ PI\ of\ \left(D-1\right)^2y=e^x\sin x$

a)

$e^x\cos x$

b)

$e^{-x}\cos x$

c)

$-e^x\sin x$

d)

$e^{-x}\sin x$

11.

$Find\ the\ PI\ of\ \left(D^2+4\right)y=x\sin x$

a)

$\frac{x}{3}\sin x-\frac{2}{9}\cos x$

b)

$x\sin x-\cos x$

c)

$x\cos x-\sin x$

d)

$\frac{2}{9}\cos x-\frac{x}{3}\cos x$

12.

$Find\ the\ PI\ of\ \left(D^2+4\right)y=\tan x\ by\ u\sin g\ method\ of\ variation\ of\ parameters$

a)

$-\cos xlox\left(\sec x+\tan x\right)$

b)

$\cos x\log\left(\sec x+\tan x\right)$

c)

$-\sin x\log\left(\sec x+\tan x\right)$

d)

$\sin x\log\left(\sec x+\tan x\right)$

13.

$Find\ the\ CF\ of\ \left(x^2D^2-xD+1\right)y=0$

a)

$Ae^{2z}+Be^z$

b)

$\left(Az+B\right)e^z$

c)

$Ae^{-z}+Be^z$

d)

$Ae^z+Be^{2z}$

14.

$Find\ the\ CF\ of\ \left(\left(x+1\right)^2D^2-\left(x+1\right)D+1\right)y=0$

a)

$\left(Az+B\right)e^z$

b)

$Ae^z+Be^{-z}$

c)

$Ae^{2z}+Be^z$

d)

$\left(Az+B\right)e^{2z}$

15.

$Find\ the\ CF\ of\ \left(Dx-y\right)=0\ ,\ \left(Dy+x\right)=0$

a)

$Ae^x+Be^{-x}$

b)

$A\cos x+B\sin x$

c)

$\left(Ax+B\right)e^x$

d)

$\left(Ax+B\right)e^{-x}$

EM-1 QUIZ 1

Total questions: 15

Worksheet time: 30mins

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