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Differential Equations

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Moderate

Inverse Laplace Transform 5

DIFFEQ-BMNYIG

Find $\mathcal{L}^{-1}\left(F(s)\right)$ if:

$$\displaystyle F(s) = \frac{1}{s^4-9s^2}$$

A

$\displaystyle \cfrac{t^3}{6} - 9t$

B

$\displaystyle \cfrac{e^{3t}}{3} - 9t$

C

$\displaystyle -\cfrac{t}{9} +\frac{1}{54} \left( e^{3t} - e^{-3t}\right)$

D

$\displaystyle -\cfrac{t}{9} +\frac{1}{54} \left( e^{3t} - e^{-3t}\right)$