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.