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Differential Equations

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Partial Fraction Decomposition and Inverse Laplace Transform

DIFFEQ-X4GJON

Joe is given the Laplace transform of a function $f(t)$, which reads $F(s)=\frac{1}{s^2-4}$.

Then, the function $f(t)$ that Joe can recover by taking the inverse Laplace transform is given by

A

$\cfrac{1}{2}\sin(2t)$

B

$e^{-4t}$

C

$\cfrac{1}{4}e^{2t}-\cfrac{1}{4}e^{-2t}$

D

None of the above