$(2)(20$ points$)$: Consider the following forced $2$ nd$-$order ordinary differential equation $($ODE$)$ modeling a dynamic system with input $u(t)$ and output $y(t)$

$y^{}+5y^{}+6y=u^{}+u.$

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.$)$

Use Matlab or another programming language to plot the step response from the previous part $($you can use built$-$in functions$).$