On the polynomial solutions of the polynomial differential equations y y' = a 0(x) + a 1(x) y + a 2(x) y 2 + … + an(x) y n

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...

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Detalles Bibliográficos
Autores: Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221356
Acceso en línea:https://ddd.uab.cat/record/221356
https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6
Access Level:acceso abierto
Palabra clave:Polynomial differential equation
Polynomial solution
Linear differential equation
Riccati differential equation
Abel differential equation
Descripción
Sumario: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.