On the general solution for the modified Emden-type equation x<SUP>..</SUP> + αxx<SUP>.</SUP> + βx<SUP>3</SUP> = O
- Chandrasekar, V. K.
- Senthilvelan, M.
- Lakshmanan, M.
DOIAbstract
In this paper, we demonstrate that the modified equation of Emden type (MEE), x.. + αxx. + βx3 = 0, is integrable either explicitly or by quadrature for any value of α and β . We also prove that the MEE possesses appropriate time-independent Hamiltonian functions for the full range of parameters α and β. In addition we show that the MEE is intimately connected with two well-known nonlinear models, namely the equation of force-free Duffing-type oscillator and the two-dimensional Lotka-Volterra equation, and thus the complete integrability of the latter two models can also be understood in terms of the MEE
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