A generalization of the Lane–Emden equation

Abstract

Singular initial value problems are investigated. We consider a new class of equations of Lane–Emden or Emden–Fowler type. The coefficient of y′ rewritten in terms of a new function ϕ (x) such that the equation can be solved in terms of ϕ. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method.

Keywords:

• Lane–Emden equations
• Emden–Fowler equations
• decomposition method

2000 AMS Subject Classification:

• 65L05
• 34B16

CCS Category:

• G.1.7