$9\mathrm{.}29.$ Consider an LTI system with input x$($t$)=$ e$-$t u$($t$)$ and impulse response h$($t$)=$

e$-2$t u$($t$).$

$($a$)$ Determine the Laplace transforms of x$($t$)$ and h$($t$).$

$($b$)$ Using the convolution property, determine the Laplace transform Y$($s$)$ of the

output y$($t$).$

$($c$)$ From the Laplace transform of y$($t$)$ as obtained in part $($b$),$ determine y$($t$).$