$4\mathrm{.}36.$ Consider an LTI system whose response to the input

x$($t$)=[$e$-$t $+$ e$-3$t$]$u$($t$)$

is

y$($t$)=[2$e$-$t$-2$e$-4$t$]$u$($t$).$

$($a$)$ Find the frequency response of this system.

$($b$)$ Determine the system's impulse response.

$($c$)$ Find the differential equation relating the input and the output of this system.