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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 orderdoi:10.1007/3-7643-7429-2_12 fatcat:2vzsec5cqrgdxmiqmteykzrq2i