The second order non-autonomous circuit of containing sometime both self-excited and forced components is a mixing oscillation. The whole network can be divided into two components

each of which can give independent phasor or algebraic equation by its own oscillation frequency

and then be solved together.The second order non-autonomous circuits are found by means of the harmonic analysis methods. Concerning the initial assumption of harmonic components

if it fits the physical characteristics of the circuit

the correct real number solution will be obtained. By contrast

the absence of real number solution implies an improper initial assumption. In this case

careful analysis and revise is necessary to reset the initial harmonic components. The nonlinear circuits of coexisting third power and fifth power is discussed in this paper. It possesses very important meaning to explain the rationality of the initial assumption of harmonic components.