$(3)[10$ points$]$ An impulsive voltage $E$ is applied at $t=0$ to a series circuit containing inductance $L$ and capacitance $C.$ Initially, the current and charge are zero. The current $i$ at time $t$ is given by:

$L\frac{di}{dt}+\frac{q}{C}=E*(t)$

Since the current $i$ is the time derivative of the charge $q,$ i$.$e$.,i=\frac{dq}{dt},$ determine an expression for the current $i$ in the circuit at time $t,$ where $q$ is the instantaneous value of the charge on the capacitor.