$(1$ point$)$ Consider the initial value problem y$"+9$y $=$ g$($t$),$ y$(0)=0,$ y$\text{'}(0)=0,$ where g$($t$)=\{$t$,$ if $0<=$t$<9$; $0,$ if $9<=$t$<$ infinity. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y$($t$)$ by Y$($s$).$ Do not move any terms from one side of the equation to the other $($until you get to part $($b$)$ below$).$