Problem $1$

Consider the system described by the following transfer function:

$\frac{Y(s)}{R(s)}=\frac{6}{(s+1{)}^2(s+4)}$

a$.$ Find the differential equation of the system.

b$.$ Derive a state$-$space representation of the system $($find $A,B,C,$ and $D$ matrices$).$

Problem $2$

For the system represented by:

$A=\left[\begin{array}{cc}-3& 1\\ -1& 2\end{array}\right],B=\left[\begin{array}{c}1\\ 1\end{array}\right],C=\left[\begin{array}{cc}1& 0\end{array}\right],D=[0]$

Find the transfer function of the system.