Algebraic general solutions of algebraic ordinary differential equations

Authors:
J. M. Aroca;J. Cano;R. Feng;X. S. Gao
Affiliations:
University de Valladolid, Valladolid, Spain;University de Valladolid, Valladolid, Spain;Institute of Systems Science, AMSS, Beijing, China;Institute of Systems Science, AMSS, Beijing, China
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE given by a differential polynomial.