Consider the initial value problem for function $y$ given by$,$

$y^{\text{'}\text{'}}-6y^{\text{'}}+18y=-4(t-2),y(0)=0,y^{\text{'}}(0)=0$

$($a$)$ Find the Laplace Transform of the source function, $F(s)=L[-4(t-2)].$

$F(s)=$

$($b$)$ Find the Laplace Transform of the solution,

$Y(s)=L[y(t)]$

$Y(s)=$

$($c$)$ Find the solution $y(t)$ of the initial value problem above.

$y(t)=$

$-4$

Recall: If needed, the step function at $c$ is denoted as $u(t-c).$