$1\mathrm{.}5$ An RC circuit with a time dependent voltage

A capacitor is initially uncharged, i$.$e$.,$ q$(0)=0$ and the system is modeled by

Kirchhoff's law:

R$($dq$)/($dt$)+(1)/($C$)$q$=$V$($t$)$

where V$($t$)$ is a time dependent applied voltage. Find the formula for the

charge on the capacitor q$($t$)$ as a function of time. Please do not assume that

the voltage V$($t$)$ is a constant. Your formula should be correct for all functions

V$($t$),$ including V$($t$)$ expressed as polynomial, exponential, and trigonometric

functions.