@**techreport**{RISC4884,author = {A. Lastra and J. R. Sendra and L. X. C. Ngo and F. Winkler},

title = {{Rational General Solution of 1-Dimensional Systems of Autonomous Ordinary Differential Equations}},

language = {english},

abstract = {An algebro-geometric method for determining the rational solvability of autonomous algebraic ordinary differential equations is extended from single equations of order 1 to systems of equations of arbitrary order but dimension 1. We provide necessary conditions, for the existence of rational solutions, on the degree and on the structure at infinity of the associated algebraic curve. Furthermore, from a rational parametrization of a planar projection of the corresponding space curve one deduces, either by derivation or by lifting the planar parametrization, the existence and actual computation of all rational solutions if they exist. Moreover, if the diferential polynomials are defined over the rational numbers, we can express the rational solutions over the same field of coeficients.
},

number = {13-09},

year = {2013},

month = {December},

keywords = {algebraic ordinary differential equations, rational solutions, parametrization of curves},

sponsor = {Austrian Science Fund (FWF): W1214-N15, project DK11},

length = {19},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}