| 1 | RATIONAL GENERAL SOLUTIONS OF HIGHER ORDER ALGEBRAIC ODES显示文摘This paper generalizes the method of Ngo and Winkler(2010,2011)for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation(AODE)to the case of a higher order AODE,provided a proper parametrization of its solution hypersurface.The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system.The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence.The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves.The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals. | HUANG Yanli NG L X Chu WINKLER Franz | 2013 | Journal of Systems Science & Complexity2013，26，2： | 3 |
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