Consider the circuit below with the switch closed $($for $\backslash (\backslash$mathrm$\{$t$\}<mn>0</mn><mtext></mtext><mi>\backslash </mi><mi>)</mi><mtext></mtext><mi>)</mi>$ and then opening at $\backslash (\backslash$mathrm$\{$t$\}=0\backslash ).$

$1.$ Calculate the initial conditions.

$2.$ For $\backslash ($ t$>0\backslash ),$ develop the differential equation for the solution using mesh analysis.

$3.$ Characterize the differential equation.

$4.$ Write the general solution.