Here we present a new approach to search for first order invariants (first integrals) of rational second order ordinary differential equations. This method is an alternative to the Darbouxian and symmetry approaches. Our procedure can succeed in many cases where these two approaches fail. We also present here a Maple implementation of the theoretical results and methods, hereby introduced, in a computational package -InSyDE. The package is designed, apart from materializing the algorithms presented, to provide a set of tools to allow the user to analyse the intermediary steps of the process. PROGRAM SUMMARYTitle of the software package: InSyDE -Invariants and Symmetries of (racional second order ordinary) Differential Equations.Catalogue number: (supplied by Elsevier) Software obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Licensing provisions: noneOperating systems under which the program has been tested: Windows 8. Programming languages used: Maple 17.Memory required to execute with typical data: 200 Megabytes. No. of lines in distributed program, including On-Line Help, etc.: 537Nature of mathematical problem Search for first integrals of rational 2ODEs. Methods of solutionThe method of solution is based on an algorithm described in this paper. Restrictions concerning the complexity of the problemIf the rational 2ODE that is being analysed presents a very high degree in (x, y, z), then the method may not work well. Typical running timeThis depends strongly on the 2ODE that is being analysed. Unusual features of the programOur implementation can find first integrals in many cases where the rational 2ODE under study can not be reduced by other powerful solvers. Besides that, the package presents some useful research commands.

No abstract