$4\mathrm{.}34.$ A causal and stable LTI system S has the frequency response

$.$ jw $+4$

H$($jw$)=62$ s$.$

$-$w $+$ JW

$($a$)$ Determine a differential equation relating the input x$($t$)$ and output y$($t$)$ of S$.$

$($b$)$ Determine the impulse response h$($t$)$ of S$.$

$($c$)$ What is the output of S when the input is

x$($t$)=$ e$-4$tu$($t$)-$te$-4$tu$($t$)?$