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An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx<sup>3</sup> = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β
Department of Physics (Formerly), Kalyani Mahavidyalaya, Kalyani, India
- 1 Department of Physics (Formerly), Kalyani Mahavidyalaya, Kalyani, India
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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 + βx<sup>3</sup> = 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.
KeywordsExact Analytical SolutionLagrangianHamiltonian
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