GATE EC 2003 Set 1 Q34 — Circuit Analysis

The circuit for $\text{Q. 33-34}$ are given in the figure. For both are the questions, assume that the switch $S$ is in position $1$ for a long time and thrown to position $2$ at $t=0$.

$I_{1}(s)$ and $I_{2}(s)$ are the Laplace transforms of $i_{1}(t)$ and $i_{2}(t)$ respectively. The equations for the loop currents $I_{1}(s)$ and $I_{2}(s)$ for the circuit shown in the figure after the switch is brought from position $1$ to position $2$ at $t=0$, are