$6\mathrm{.}26$ The two parallel inductors shown are connected across the terminals of a black box at $t=0$ The resulting voltage $v$ for $t>0$ is known to be $12e^{-t}V.$ It is also known that $i_1(0)=2$A and $i_2(0)=4A.$

a$.$ Replace the original inductors with an equivalent inductor and find $i(t)$ for $t0.$

b$.$ Find $i_1(t)$ for $t0.$

c$.$ Find $i_2(t)$ for $t0.$

d$.$ How much energy is delivered to the black box in the time interval

e$.$ How much energy was initially stored in the parallel inductors?

f$.$ How much energy is trapped in the ideal inductors?

g$.$ Show that your solutions for $i_1$ and $i_2$ agree with the answer obtained in $(f)$