An electric circuit contains a resistance R and a capacitor C in series, and a battery supplying a time-varying electromotive force V(t). The charge q on the capacitor therefore obeys the equation R(dq/dt) + q/C = V(t). Assume that initially there is no charge on the capacitor, and given that V(t) = V0 sin(t).
(a) Find the Integrating Factor for the above equation.
(b) Solve the differential equation.
Hint: You might find using q(0) = 0 useful.