Consider the following initial value problem: $$y'' + {9} y= \begin{cases} 6 t, & 0 \leq t < 3 \cr 0, & t \geq 3 \end{cases} \hspace{0.5in} y(0)=0, \hspace{0.05in} y'(0)=0$$

Using $Y$ for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L} \lbrace y(t) \rbrace$,
find the equation you get by taking the Laplace transform of the differential equation and solve for
$Y(s) =$