Write the differential equation of charge for $L-C-R$ series $AC$ circuit.

(N/A) In an $L-C-R$ series circuit,the sum of potential drops across the inductor $(L)$,resistor $(R)$,and capacitor $(C)$ is equal to the applied electromotive force $(E(t))$.
According to Kirchhoff's voltage law:
$L \frac{dI}{dt} + IR + \frac{q}{C} = E(t)$
Since the current $I = \frac{dq}{dt}$,the rate of change of current is $\frac{dI}{dt} = \frac{d^2q}{dt^2}$.
Substituting these into the equation,we get:
$L \frac{d^2q}{dt^2} + R \frac{dq}{dt} + \frac{q}{C} = E(t)$
This is the second-order linear differential equation for the charge $q$ in an $L-C-R$ series circuit.