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.