The state$-$space representation of a dynamical system is given as follows:

x$\_($t$)=$ Ax$($t$)+$ Bu$($t$)$

y$($t$)=$ Cx$($t$)+$ Du$($t$)$

where A $=$

$01$

$02$

$,$ B $=$

$1$

$1$

$,$ C $=$

$21$

$,$ D $=0$ and x$0=$

$2$

$3$

$.$

a$)$ Compute x$($t$)$ and y$($t$)$ for u$($t$)=1+2$e$2$t$.$

b$)$ Compute x$(1)$ and y$(1)$ for t $!1.$ Comment about your results.