Problem $2$: The switch has been open for a long time. At t $=0$ the switch is closed.

w

iL$(1)$

$200$

t$=0$

$2$ V

$000$

$50$ mH

a$)$ Determine the initial current i$2(0).$

b$)$ Find the differential equation for i$($t$)$

c$)$ Transform the equation into s domain and obtain I$12($S$).$

d$)$ Determine i$($t$).$