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@inproceedings{Eremenko1998RationalSO, title={Rational Solutions of First-order Differential Equations}, author={A. Eremenko}, year={1998} }

- Published 1998

We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz, w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation (1) F (w′, w, z) = 0 (w′ = dw/dz) where F is a polynomial in three variables. Theorem 1. For every F there exists a constant C = C(F ) such that the degree of every rational solution w of (1… CONTINUE READING