Free Printable EM-1 PET-1

1.

$Find\ the\ CF\ of\ \left(D^2-6D+13\right)y=0$

a)

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

b)

$e^{3x}\left(A\cos2x+B\sin2x\right)$

c)

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

2.

$Solve\ \left(D^3-6D^2+11D-6\right)y=0$

a)

$Ae^x+\left(Bx+C\right)e^{2x}+De^{3x}$

b)

$Ae^x+\left(B\cos2x+B\sin2x\right)$

c)

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

3.

$Solve\ \frac{d^2y}{dx^2}-6\frac{dy}{dx}+9y=0$

a)

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

b)

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

c)

$e^x\left(A\cos2x+B\sin2x\right)$

4.

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

a)

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

b)

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

c)

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

5.

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

a)

$\frac{e^{\left(\log2\right)x}}{\left(\log2-2\right)^2}$

b)

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

c)

$\frac{e^{\left(\log x\right)}}{\left(\log2-2\right)^2}$

6.

$Find\ the\ PI\ of\ \left(D^3-4D\right)y=2\cosh2x$

a)

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

b)

$\frac{x}{8}\left(e^{2x}+e^{-2x}\right)$

c)

$\frac{xe^{2x}}{8}$

7.

$Find\ the\ PI\ \left(D^2+16\right)y=\cos4x$

a)

$\frac{x\sin4x}{8}$

b)

$\frac{\sin4x}{8}$

c)

$x\sin x$

8.

$Find\ the\ PI\ of\ \left(D^3+1\right)y=\cos2x$

a)

$\frac{1}{65}\left(\cos2x-8\sin2x\right)$

b)

$\left(\cos2x+\sin2x\right)$

c)

$\frac{1}{65}\left(\cos2x+8\sin2x\right)$

9.

$Find\ the\ PI\ of\ \left(D^2+3D+2\right)y=4\sin x$

a)

$\frac{2}{5}\left(\sin x-3\cos x\right)$

b)

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

c)

$\frac{5}{2}\left(3\cos x+\sin x\right)$

10.

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

a)

$\frac{1}{2}\left(x^2-3x+\frac{7}{2}\right)$

b)

$\left(x^2-3x+\frac{7}{2}\right)$

c)

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

11.

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

a)

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

b)

$\frac{x^2}{3}+4x$

c)

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

12.

$Find\ the\ PI\ of\ \left(D^2+2D+3\right)y=5x^2$

a)

$\frac{5}{3}\left[x^2-\frac{4}{3}x+\frac{2}{9}\right]$

b)

$\frac{5}{2}\left[x^2+\frac{2}{9}\right]$

c)

$\frac{5}{3}\left[x^2+\frac{4}{3}x-\frac{2}{9}\right]$

13.

$Find\ the\ PI\ of\ \left(D^3-3D^2+3D-1\right)y=x^2e^x$

a)

$\frac{e^xx^5}{60}$

b)

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

c)

$\frac{e^x}{60}$

14.

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

a)

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

b)

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

c)

$\frac{e^x\cos2x}{2}$

15.

$Find\ the\ PI\ of\ \left(D^2+5D+4\right)y=e^{-x}\sin2x$

a)

$-\frac{1}{26}e^{-x}\left(3\cos2x+2\sin2x\right)$

b)

$\frac{1}{26}e^{-x}\left(3\cos2x+2\sin2x\right)$

c)

$e^{-x}\left(3\cos2x+2\sin2x\right)$

16.

$Find\ the\ PI\ of\ \frac{d^2x}{dt^2}+2\frac{dx}{dt}+3t=t\cos t$

a)

$\frac{1}{4}\left(t-1\right)\left(\cos t+\sin t\right)$

b)

$\frac{1}{4}\left(\cos t+\sin t\right)$

c)

$\left(t-1\right)\left(\cos t+\sin t\right)$

17.

$Find\ the\ PI\ of\ \left(D^2+4D+4\right)y=xe^{-2x}$

a)

$\frac{e^{-2x}x^3}{6}$

b)

$\frac{e^{2x}x^3}{6}$

c)

$-\frac{e^{-2x}x^3}{6}$

18.

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

a)

$A\cos x+B\sin x$

b)

$A\cos x-B\sin x$

c)

$\frac{1}{3}\left(A\cos x+B\sin x\right)$

19.

$Find\ the\ CF\ of\ \left(D^2+3D+4\right)y=2$

a)

$e^{-\frac{3x}{2}}\left[A\cos\frac{\sqrt{7}}{2}x+B\sin\frac{\sqrt{7}}{2}x\right]$

b)

$e^{\frac{3x}{2}}\left[A\cos\sqrt{7}x+B\sin\sqrt{7}x\right]$

c)

$e^{-\frac{3x}{4}}\left[A\cos\frac{7}{2}x+B\sin\frac{7}{2}x\right]$

20.

$Find\ the\ CF\ of\ \left(D^3-3D^2+4D-2\right)y=\cos^2x$

a)

$e^x\left[A+B\cos x+C\sin x\right]$

b)

$\left(A+Bx\right)e^x+C\cos x$

c)

$Ae^x+e^x\left(A\cos2x+B\sin2x\right)$

EM-1 PET-1

Total questions: 20

Worksheet time: 3600secs

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