Problem $5$: $($Exercise $7\mathrm{.}1$ in the lecture notes part $4,$ page $18)$

$7\mathrm{.}1$ The switch in the circuit shown has been closed for a long time and is opened at $\backslash ($ t$=0\backslash ).$

a$)$ Calculate the initial value of $\backslash ($ i $\backslash ).$

b$)$ Calculate the initial energy stored in the inductor.

c$)$ What is the time constant of the circuit for $\backslash ($ t$>0\backslash )?$

d$)$ What is the numerical expression for $\backslash ($ i$($t$)\backslash )$ for $\backslash ($ t $\backslash$geq $0\backslash )?$