A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations
Mathematical Physics
2008-10-02 v1 Classical Analysis and ODEs
math.MP
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 \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.
Cite
@article{arxiv.math-ph/0506037,
title = {A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations},
author = {J. Avellar and L. G. S. Duarte and S. E. S. Duarte and L. A. C. P. da Mota},
journal= {arXiv preprint arXiv:math-ph/0506037},
year = {2008}
}