discrete$-$time LTI system is defined by the following difference equation:

y$[$n$]=$ x$[$n$]$ x$[$n $1]+$ x$[$n $2]$ x$[$n $3].$

Suppose that the input to this system is x$[$n$]=$ $[$n $4]+$ u$[$n$]+$ cos

$2$ n$.$ u$[$n$]$ is the unit step signal

defined as

u$[$n$]=$

$($

$0$ n $<0$

$1$ n $0.$

Determine the output of the system.