$($Laplace transform$)$ Consider a causal LTI system for which the input $x(t)$ and output $y(t)$ are related by the differential equation

$\frac{d^{2}y(t)}{d{t}^2}+3\frac{dy(t)}{dt}+2y(t)=x(t)$

Let $H(s)$ be the Laplace transform of impulse response $h(t)$ and solve the following.

$($a$)$ Determine $H(s)$ and sketch the ROC of $H(s).$

$($b$)$ Find $y(t)$ when $x(t)=e^{3t}u(t).$