Problem $3.$ In the circuit shown below, the initial currents in inductors $L_1$ and $L_2$ have been established by sources not shown. The switch is opened at $t=0.$

$($a$)$ Find $i_1,i_2$ and $i_3$ for $t0.$

$($b$)$ Calculate the initial energy stored in the parallel inductors.

$($c$)$ Determine how much energy is stored in the inductors as $t.$

$($d$)$ Show that the total energy delivered to the resistive network equals the difference between the results obtained in $($b$)$ and $($c$).$