A note on integration of the Emden-Fowler equation

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