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Differential Equations

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Moderate

Step Function 5

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

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

A

$$ -\frac{t}{3} + \left( e^{t} - e^{-t}\right)$$

B

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

C

$$ -\frac{t}{9} +\frac{t}{9} \left( e^{t} - e^{-t}\right)$$

D

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