@techreport{RISC4039,author = {Y. Huang and L. X. Chau Ngo},
title = {{Rational General Solutions of High Order Non-autonomous ODEs}},
language = {english},
abstract = {In this paper, we generalize the results of Ngo and Winkler [18, 20, 21] to the case of
high order non-autonomous algebraic ODE with a birational parametrization of the corre-
sponding algebraic hypersurface. First, we reduce the problem for finding rational general
solutions of non-autonomous n -1 (n > 2) order ODE to finding rational general solutions
of an associated first order rational system of autonomous ODEs in n indeterminates based
on the parametrization of hypersurface. Next, the correspondence of the rational general
solutions between the original non-autonomous algebraic ODE and the associated system
of autonomous ODEs is proved. Finally, a criterion is presented for existence of rational
general solutions of the associated system of autonomous ODEs if the degree bound of its
rational general solutions is given. Moreover, we give some nice properties of polynomial
system of autonomous ODEs.},
number = {10-13},
year = {2010},
month = {June},
keywords = {Rational general solutions, non-autonomous ODE, associated system of autonomous ODEs, hypersurface, parametrization.},
length = {15},
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)}
}