The paper deals with the analysis of RL and RC circuits by using linear ordinary differential equation of first order. Two circuits that consist of a single closed loop containing a resistor(R) and either a capacitor(C) or an inductor(L) connected to a power source ( or voltage source ) in series will be analyzed. Applying Kirchoff laws on voltage and current, a differential equation is formed. The general solution of the differential equation has two parts complementary function (CF) and particular integral (P.I) in which (CF) represents transient response and (P.I) represents steady response. The general solution of a differential equation represents the complete response of network.