In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) associated to a rational second order ordinary differential equation (rational 2ODE) that is linked to the search of an integrating factor. In this work we investigate the relation between these S-functions and the Lie symmetries of a rational 2ODE. Based on this relation we can construct a semi-algorithmic method to find the Lie symmetries of a 2ODE even in the case where it presents no Lie point symmetries.
@article{arxiv.1007.2861,
title = {A Semi-Algorithmic Search for Lie Symmetries},
author = {L. G. S. Duarte and L. A. C. P. da Mota},
journal= {arXiv preprint arXiv:1007.2861},
year = {2010}
}