title: Rational general solutions of planar rational systems of autonomous ODEs.
abstract: In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case.
authors.affiliation: DK Computational Mathematics, Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria.
authors.forename: L X
authors.initials: LX
authors.lastname: Châu Ngô
authors.affiliation: Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria.
authors.forename: Franz
authors.initials: F
authors.lastname: Winkler
keywords: Invariant algebraic curves; Ordinary differential equations; Rational first integrals; Rational parametrizations; Rational solutions