A Feasible Algorithm for Lagrangian and Hamiltonian description of the modified Emden Equation

We examine a method to solve second-order ordinary differentialequations by generalizing the approach based on Duarte’s algorithm forfirst-order ordinary differential equations. This new generalized methodis introduced by Prelle-Singer and they obtain integrals from a singleintegral. The first integral I(t, x, x') of the modified Emden equation isfound and obtain an analytical solution by these first integral. Finally,the exact solutions corresponding to the physically different cases areobtained and represented graphically. All diagrams and solutions havebeen made with Mathematica and C++ programming language.

Keywords:

Lagrangian and Hamiltonian forms , Useful algorithm , Differential equations , First integrals , modified Emden equation