#$2$: Consider a stable and causal continuous time system whose input $x(t)$ and output $y(t)$ are related by the following difference equation:

The input $x(t)$ is:

$y(t)-\frac{1}{2}y(t-1)=x(t)$

$x(t)=sinc(t)=\frac{sint}{t}$

$($a$)$Sketch the output $y(t).$

$($b$)$Determine an analytic expression for the output $y(t).$