On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn

Antoni Ferragut () and Jaume Llibre ()
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Antoni Ferragut: Universidad Internacional de la Rioja
Jaume Llibre: Universitat Autònoma de Barcelona

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 217-232

Abstract: Abstract In this paper we deal with differential equations of the form yy′ = P(x, y) where y′ = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions.

Keywords: Polynomial differential equation; polynomial solution; linear differential equation; Riccati differential equation; Abel differential equation; 34A05; 34A34; 34C05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0396-6

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