A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations
Abstract
Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure ManMac,firsTHEOps1,secondTHEOps1. Apart from practical computational considerations, the method will be capable of telling us (up to a certain polynomial degree) if the SOODE has an elementary first integral and, in positive case, finds it via quadratures.
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