Take the Laplace transform of the following initial value problem and solve for $Y(s) = \mathcal{L}\lbrace y(t) \rbrace$: $$y'' + {6} y' + {17} y= T(t) \hspace{0.5in} y(0)=0, \; y'(0)=0$$

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

$Y(s)=$ .
Graph of $T(t)$ (a triangular wave function):