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

Antoni Ferragut; Jaume Llibre

doi:10.1007/s13226-020-0396-6

On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a ₀(x) + a ₁(x) y + a ₂(x) y ² + … + a_n(x) y ⁿ

Antoni Ferragut^*, Jaume Llibre

^*Autor correspondiente de este trabajo

Universidad Internacional de La Rioja

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

3 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	217-232
Número de páginas	16
Publicación	Indian Journal of Pure and Applied Mathematics
Volumen	51
N.º	1
DOI	https://doi.org/10.1007/s13226-020-0396-6
Estado	Publicada - 1 mar 2020

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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 = "Abel differential equation, Polynomial differential equation, Riccati differential equation, linear differential equation, polynomial solution",

author = "Antoni Ferragut and Jaume Llibre",

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AU - Llibre, Jaume

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - Abel differential equation

KW - Polynomial differential equation

KW - Riccati differential equation

KW - linear differential equation

KW - polynomial solution

UR - https://www.scopus.com/pages/publications/85081719192

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ER -

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

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On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a ₀(x) + a ₁(x) y + a ₂(x) y ² + … + a_n(x) y ⁿ