Consider the following forced $2$nd$-$order ordinary differential equation $($ODE$)$ modeling a dynamic system with input u$($t$)$ and output y$($t$)$

y$+5$y $+6$y $=$u $+$ u$.$

$$ Determine the transfer function from the input u to the output y$.$ Is the system stable?

Justify your answer.

$$ Determine the dynamic response of the output y$($t$)$ to a unit step input. $($Hint: Partial

fraction expansion.$)$