Integrating factors and λ-symmetries

Abstract

We investigate the relationship between integrating factors and λ-symmetries for ordinary differential equations of arbitrary order. Some results on the existence of λ-symmetries are used to prove an independent existence theorem for integrating factors. A new method to calculate integrating factors and the associated first integrals is derived from the method to compute λ-symmetries and the associated reduction algorithm. Several examples illustrate how the method works in practice and how the computations that appear in other methods may be simplified. Copyright © 2008 by C Muriel and J L Romero.