Lam Xuan Chau Ngo, Franz Winkler,
"Rational general solutions of planar rational systems of autonomous ODEs"
, in Journal of Symbolic Computation, Vol. 46, Nummer 10, Seite(n) 1173-1186, 2011, ISSN: 0747-7171
Rational general solutions of planar rational systems of autonomous ODEs
Sprache des Titels:
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.