Difficult# Charging Capacitor in a Circuit

APPHEM-3GDZE9

A Circuit contains a resistor of resistance $\mathit{R}$ and a capacitor $C_1$ of capacitance $\mathit{C}$, a second Capacitor $C_2$ of capacitance $\mathit{2C}$, and a battery that provides an emf of $V$, as shown above.

Initially, both switches are open and both capacitors are uncharged. At time $t=0$, switch 1 is closed. What is the charge as a function of time?