$($Total: $30$ points$)$ b Adapted from $[$Am$]17\mathrm{.}28$: Find the zero$-$state response, the zero$-$input response,

and the total response $($all in the time domain$)$ of the following systems using the z$-$transform:

$($a$)(15$ points$)$ y$[$n$]+1\mathrm{.}5$y$[$n $1]+0\mathrm{.}5$y$[$n $2]=(0\mathrm{.}5)$nu$[$n$]$ with y$[1]=0$ and y$[2]=4.$

$($b$)(15$ points$)$ y$[$n$]$ y$[$n $1]+0\mathrm{.}5$y$[$n $2]=(0\mathrm{.}5)$nu$[$n$]$ with y$[1]=1$ and y$[2]=2$