A system is described by the following second$-$order linear differential equation d$2$ y dt$2+5$ dy dt $+6$y $($t$)=$ x $($t$)$ where y$(0-)=-1,$ y$\text{'}(0-)=5,$ and the input x $($t$)=$ sin$(2$t$)$u$($t$)+$etu$($t$)1.$ By taking the Laplace Transform of both sides of the equation above, express Y$($s$)$ the Laplace Transform of y$($t$)$ in terms of X$($s$)$ the Laplace Transform of x$($t$)$ and the initial conditions y $(0-)$ and y$\text{'}(0-).(10$ points$)$ Y$(8)2.$ Find the transfer function H $($s$)$ The transfer function is defined when there are X$($s$)$ no initial conditions. $(10$ points$)3.$ Solve the differential equation by finding the inverse Laplace Transform of Y$($s$)$ found in part $1$ of this question. $(10$ points$).$