Consider an LTI system whose response to the input

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

is

$y(t)=[2e^{-1}-2e^{-4t}]u(t)$

$($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.

Please do not use laplace transform