We study the rational general solutions of a nonautonomous algebraic ordinary differential equation (ODE) of order 1. The geometric approach of R. Feng and X-S. Gao ([FG04], [FG06]) in the autonomous case can be extended to the non-autonomous ODEs of order 1 in a natural way provided a proper rational parametrization of the corresponding algebraic surface. The work leads to studying a system of autonomous ODEs of order 1 and of degree 1. We call it the associated system with respect to a parametrization of the original ODE. If we can solve this associated system for its rational general solutions, then we shall obtain the rational general solutions of the original ODE by using the parametrization map.
Erscheinungsjahr = 2010