Kirchhoff's Laws on Series-Parallel Circuit
I think it should be like this:

\$I=I_{2}+I_{1}\$ 

\$I_{1}=I_{3}+I_{4}\$

\$\$

\$V=V_{C_{1}}+V_{R_{1}}\$

\$V=\frac{1}{C_{1}}\int I_{2}\mathrm{d}t+R_{1}I\$

\$\$

\$V_{R_{2}} = V_{C_{1}}\$

\$R_{2}I_{3} = \frac{1}{C_{1}}\int I_{2}\mathrm{d}t\$

\$\$

\$V_{R_{2}}=V_{R_{3}}+V_{C_{2}}\$

\$\$

\$V_{R_{3}}+V_{C_{2}}=V_{R_{2}}\$

\$R_{3}I_{4}+\frac{1}{C_{2}}\int I_{4}\mathrm{d}t=R_{2}I_{3}\$

The rest should be a math excercise, I think :-)