EXERCISE E$4\mathrm{.}7$

For an LTIC system with transfer function

H$($s$)=5+552+45+3$

$($a$)$ Describe the differential equation relating the input x$($t$)$ and output y$($r$).$

$($b$)$ Find the system response y$($t$)$ to the input x$($t$)=$ e$^2$u$($t$)$ if the system is initially in zero state.

ANSWERS

dydy $(8)+4+3$y$($t$)=$ dx $+5$x$($t$)$

$($b$)$ y$($t$)=(2$e$3$e$2+$e$-3)$u$($t$)$