$10\mathrm{.}12$ Consider a discrete$-$time LTI system represented by the difference equation

with the given initial condition

where x$[$n$]$ is the input and y$[$n$]$ the output.

Suppose the input of the system is x$[$n$]=(1+0\mathrm{.}5$n cos$($n$))$u$[$n$].$

Determine the steady$-$state response yss$[$n$].$ If the initial condition is

changed, would you get the same steady$-$state response? Explain.