Transient and steady state response of RC circuit?

To evaluate the transient response of an RC circuit, you start with the steady state just prior to the transient, i.e. just prior to the switch being opened or closed, or just prior to whatever transient event you are modeling. Since you are steady state, assume that capacitors are not present, i.e. they are resistors with infinite impedance. Calculate the voltage and current at each node, using Ohm's law and/or Kirchoff's law and/or Norton/Thevanin equivalents as necessary. Remember that capacitors resist a change in voltage. The equation is dv/dt = i/c. At t=0, assume that each capacitor has the voltage calculated from the initial steady state condition. Initiate the transient and calculate the voltage and current at each node using the initial state differential equation. You can do this analytically, or you can model it in software. If you model, pick an appropriate delta-T, and do a step wise evaluation until the voltages and current settle to their new values. Adjust delta-T to make sure that you are getting consistent results. Just don't go too short, as truncation error can bias the results.