A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations

Avellar, J.; Duarte, L. G. S.; Duarte, S. E. S.; da Mota, L. A. C. P.

A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations

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Description

Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure \cite{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.