Power series approach to nonlinear oscillators

In this article, we introduce a nonlinear oscillator equation containing two strong linear terms. An approximate solution was obtained using power series approach. Furthermore, by introducing a parameter to the original equation, we fined the fixed points of the modified nonlinear oscillator equation and study stability analysis of these fixed points. On the other hand, we simulate the solution of the nonlinear oscillator equation and introduced many plots for different initial conditions. Finally, we make some plots concerning the phase portrait for different cases.