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

Bahar Milani¹ Özlem ORHAN²

1) Department of Computer Engineering, Bandirma Onyedi Eylul University, Balikesir- Turkey Email:
2) Department of Engineering Basic Science, Bandirma Onyedi Eylul University, Balikesir- Turkey Email:

Publication : 10th International Conference on Innovative Technologies in Science, Engineering and Technology(tetsconf.com)
Abstract :
We examine a method to solve second-order ordinary differential equations by generalizing the approach based on Duarte’s algorithm for first-order ordinary differential equations. This new generalized method is introduced by Prelle-Singer and they obtain integrals from a single integral. The first integral of the modified Emden equation is found and obtain an analytical solution by these first integral. Finally, the exact solutions corresponding to the physically different cases are obtained and represented graphically. All diagrams and solutions have been made with Mathematica and C++ programming language
Keywords : Lagrangian and Hamiltonian forms Useful algorithm Differential equations First integrals modified Emden equation