a$)[10]$ Consider a DT system describe by the block diagram given below:

Assume the system is casual and initially at REST condition:

$($a$)[3]$ Determine the difference equation relating $y[n]$ with $x[n]$

$($b$)3$ Assume $x[n]=u[n]$ determine $y[-5],y[1]$ and $y[3]$ by solving the difference equation recursively

$($c$)[2]$ Assume $x[n]=[n],$ determine the general solution $y[n]$ by solving the difference equation recursively

$($d$)[2]$ Determine the close form equation for the impulse response $h[n]$ using part$($c$)$ only.