Total response of a first order RC circuit
At the steady state there will be no current flowing because the capacitor is an open circuit for DC. Then your voltage accross the resistor will be 0.

So Vp is distributed accross both capacitors. But because these capacitors are in series, they will have the same charge.

So basically you have: Q = C1.V1 = C2.V2 and V1 + V2 = Vp

From these two equations you can then compute V1 and V2.