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https://doi.org/10.1063/1.1920287

has been cited by the following article:

• TITLE: An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx3 = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β

  AUTHORS: D. Biswas

  KEYWORDS: Exact Analytical Solution, Lagrangian, Hamiltonian

  JOURNAL NAME: Natural Science, Vol.11 No.1, January 17, 2019

  ABSTRACT: The modified Emden-type is being investigated by mathematicians as well as physicists for about a century. However, there exist no exact explicit solution of this equation, ẍ + αxẋ + βx3 = 0 for arbitrary values of α and β. In this work, the exact analytical explicit solution of modified Emden-type (MEE) equation is derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of MEE are also worked out. The solution is also utilized to find exact explicit analytical solution of Force-free Duffing oscillator-type equation. And exact explicit analytical solution of two-dimensional Lotka-Volterra System is also worked out.