On the discrete group analysis for solving some classes of Emden-Fowler equations

This paper presents an account of the fundamentals of the discrete group approach for analysis and integration of practical nonlinear ordinary differential equations. In this paper, by means of appropriate transformations of discrete group analysis, some classes of second-order differential equations of Emden-Fowler type is transformed into the other solvable class. For this purpose, we give some applicable relations between the Emden-Fowler and Lane-Emden equations, in order to solve some classes of Emden-Fowler equations. This approach is effective in finding a great number of new integrable equations which thus far could not be integrated using the classical methods.