Take the Laplace transform of the following initial value problem and solve for $Y(s) = \mathcal{L}\lbrace y(t) \rbrace$: $$y'' -{6} y' - {27} y= S(t) \hspace{0.5in} y(0)=0, \; y'(0)=0$$

Where $S(t) = \begin{cases} 1, & 0 \leq t < 1 \cr 0, & 1 \leq t < 2 \end{cases} ,\hspace{0.2in} S(t+2) = S(t)$.

$Y(s)=$ .
The graph of $S(t)$ (a square wave function):