Exercise $4(10$ points$)$

Evaluate

$L^{-1}[\frac{s}{(s2)(s^{2}4)}]$

Possible Answers

$($a$.)y=\frac{1}{4}cos(2t)\frac{1}{4}sin(2t)-\frac{1}{4}{e}^{-2t}$

$($b$.)y=\frac{1}{4}cos(2t)\frac{1}{4}sin(2t)\frac{1}{4}{e}^{-2t}$

$($c$.)y=\frac{1}{4}cos(2t)\frac{1}{4}{e}^{-2t}sin(2t)$

$($d$.)y=\frac{1}{4}{e}^{-2t}cos(2t)\frac{1}{4}sin(2t)$

$($e$.)$ None of the above

Show your work.