Problem $1$: System Response from I$/$O Equation

Problem $1\mathrm{.}1$ Consider the following system represented by I$/$O equation.

$y^{}+3y^{}+2y=u$

Find the unit impulse response $y(t)$ using Laplace Domain approach, assuming all initial

conditions are zero.

Find the unit step response $y(t)$ using Laplace Domain approach, assuming all initial con$-$

ditions are zero.

Find the system response $y(t)$ to the input $u(t)=3e^{-t}$ with initial conditions $y(0)=1,y^{}(0)=$

$1,$ using Laplace Domain approach.