Rational General Solutions of Trivariate Rational Systems of Autonomous ODEs

摘要

We generalize the method of Ngo and Winkler [5] for finding rational general solutions of a plane rational differential system to the case of a trivariate rational differential system. We give necessary and sufficient conditions for the trivariate rational differential system to have a rational solution based on proper reparametrization of invariant algebraic space curves. We also present a criterion for a rational solution to be a rational general solution.