A Maple package to find first order differential invariants of 2ODEs via a Darboux approach. ere we present an implementation of a semi-algorithm to find elementary first order differential invariants (elementary first integrals) of a class of rational second order ordinary differential equations (rational 2ODEs). The algorithm was developed in [L. G. S. Duarte and L. A. C. P. da Mota, J. Math. Phys. 50, No. 1, 013514, 17 p. (2009; Zbl 1200.34039)]; it is based on a Darboux-type procedure, and it is an attempt to construct an analog (generalization) of the method built by M. J. Prelle and M. F. Singer [Trans. Am. Math. Soc. 279, 215–229 (1983; Zbl 0527.12016)] for rational first order ordinary differential equations (rational 1ODEs). to deal, this time, with 2ODEs. The FiOrDi package presents a set of software routines in Maple for dealing with rational 2ODEs. The package presents commands permitting research investigations of some algebraic properties of the ODE that is being studied.
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- Avellar, J.; Duarte, L.G.S.; da Mota, L.A.C.P.: A Maple package to find first order differential invariants of 2ODEs via a Darboux approach (2014)