Rational general solutions of planar rational systems of autonomous ODEs (Q719763)

A method is presented to compute rational solutions of rational systems of ODEs in the form \[ \dot{x}=A(x,y)/B(x,y),\;\;\dot{y}=C(x,y)/D(x,y). \] The method is based mainly on a proper rational parametrization of systems' rational invariant algebraic curves. Also, an algorithm to construct a rational general solution from a given rational first integral of the system is proposed.