$(15$ points$)$

$($a$)$ Find the general solution of the equation $y^{\text{'}\text{'}}+2y^{\text{'}}-3y=0.$

$($b$)$ Find the solution to the initial value problem $y^{\text{'}\text{'}}+2y^{\text{'}}+y=0$ where $y(0)=1$ and $y^{\text{'}}(0)=-3.$