Consider a system described by the following differential equation with the given initial conditions.

y$+10$y$+9$y$=$f$($t$),$ y$(0)=0,$y$(0)=2$

$($a$)$ What is the transfer function of the system, H$($s$)?$

$($b$)$ What is the impulse response of the system, h$($t$)?$

$($c$)$ Use Laplace transform to obtain a solution for y$($t$)$ when the input is f$($t$)=9$tu$($t$).$

Show detailed steps.$$