$(30$ points$)$ For the electric system given below, the switch is in a closed position for a long time before $t=0,$ when it is opened instantaneously.

$($a$)(5$ points$)$ Find the initial conditions for the capacitor voltage and the inductor current.

$($b$)(5$ points$)$ Establish the s$-$domain circuit for $t0.$

$($d$)(10$ points$)$ Find the zero$-$input response of the inductor current $i(t)$ for $t0.$

$($e$)(10$ points$)$ Find the zero$-$state response of the inductor current $i(t)$ for $t0.$