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Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations [chapter]

Guoting Chen, Yujie Ma
Trends in Mathematics  
Algebraic differential equations of the first order are considered. An effective necessary condition for an algebraic differential equation of the first order to have a general rational solution is given: the algebraic genus of the equation should be 0. Combining with Fuchs' conditions for algebraic differential equations without movable critical points, an algorithm is given for the computation of rational solutions of these equations. It is based on an algorithmic reduction of first order
more » ... of first order algebraic differential equations with genus 0 and without movable critical point to classical Riccati equations.
doi:10.1007/3-7643-7429-2_12 fatcat:2vzsec5cqrgdxmiqmteykzrq2i