Problem $1-$ CTFT and Differential Equations $[20$ pts$]$

A causal and stable LTI system S has the frequency response

H$($j$\backslash$omega $)=($j$\backslash$omega $+4)/(6-\backslash$omega $^(2)+5$j$\backslash$omega $).$

$($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$^(-4$t$)$u$($t$)-$te$^(-4$t$)$u$($t$)?$