On General Solutions of Polytropes of Lane-Emden Equation in (r, P) Variables: A Review

Nonlinear singular differential equations are challenging to solve, and they frequently have no accurate solution. It is only logical to search for the presence of the analytical solution and numerical solution since the exact solution does not exist. In this work we focused on both sides of nonlinear singular boundary value problems (SBVPs) and discussed various analytical and numerical approaches that have been developed to handle a class of nonlinear singular differential equations. Solution of Lane - Emden equation have generally been considered in (xi, theta) variables. It is shown that r and P are the only suitable variables for the study of the structure of polytrophic configuration near the origin in the form of a series for radius r < 1 of the Lane-Emden equation.