An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx3 = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β ()
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.
Share and Cite:
Biswas, D. (2019) An Analysis of Modified Emden-Type Equation ẍ + αxẋ + βx
3 = 0: Exact Explicit Analytical Solution, Lagrangian, Hamiltonian for Arbitrary Values of α and β.
Natural Science,
11, 8-16. doi:
10.4236/ns.2019.111002.