A note on integration of the Emden-Fowler equation. (English) Zbl 0562.34002

Rosenau, Philip

Int. J. Non-Linear Mech. 19, 303-308 (1984).

Summary: Using a simple change of variables, the Emden-Fowler equation, \((x^{\nu +\alpha}y')'+ax^{\nu}y^ n=0\) is shown to be integrable provided that either of the constraints \((\nu +\alpha -1)n=3-\alpha +\nu\) or \((\nu +\alpha -1)n=3-2\alpha -\nu\) is satisfied. Every integrable case generates a one parameter family of integrable Emden-Fowler equations.

MSC:

34A05	Explicit solutions, first integrals of ordinary differential equations
34C20	Transformation and reduction of ordinary differential equations and systems, normal forms

Keywords:

Emden-Fowler equation