Not a math solution but a simulation.
\$Z = R_1+Z_{C_1} + R_2//Z_{C_2} =R_1+Z_{C_1} + \dfrac{R_2*Z_{C_2}}{R_2+Z_{C_{2}}} \$
\$I_o=V_o/Z = \dfrac{R_2+Z_{C_2}}{R_1+Z_{C_1}+R_2*Z_{C_2}}\$
You can also simulate it and interactively change any component value to correlate your theoretical understanding of Bode Plots and transient Time response.
It's just an equivalent impedance ratio using capacitor impedances and initial conditions using KVL KCL. Normally one might use a current source to measure voltage as impedance. I started with 10k and a voltage source. As all the Caps short out at HF & what's left is the single series 10R as my flat curve.

