On the general solution for the modified Emden type equation $\ddot{x}+\alpha x\dot{x}+\beta x^3=0$

摘要: In this paper, we demonstrate that the modified Emden type equation (MEE), $\ddot{x}+\alpha x\dot{x}+\beta x^3=0$, is integrable either explicitly or by quadrature for any value of $\alpha$ and $\beta$. We also prove MEE possesses appropriate time-independent Hamiltonian function full range parameters addition, show intimately connected with two well known nonlinear models, namely force-free Duffing oscillator dimensional Lotka-Volterra (LV) thus complete integrability latter models can be understood in terms MEE.