Consider a system described by the input output equation

d$2$y$($t$)$

dt$2+8$ dy$($t$)$

dt $+17$y$($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$)$