Question $2.$ Consider a system described by the input output equation $10$ d $2$ y$($t$)$ dt$2+31$ dy$($t$)$ dt $+15$y$($t$)=$x$($t$)2$x$($t$).(1)(2$a$)$ Find the zero$-$input response yzi$($t$)$ of the system under the initial condition y$(0)=3$ and y$(0)=2.(2$b$)$ Find the zero$-$state response yzs$($t$)$ of the system to the unit step input x$($t$)=$ u$($t$).(2$c$)$ Find the solution y$($t$)$ of $(1)$ under the initial condition y$(0)=3$ and y$(0)=2$ and the input x$($t$)=$ u$($t$).$