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

^*Corresponding author for this work

Universidad Internacional de La Rioja (UNIR)

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	217-232
Number of pages	16
Journal	Indian Journal of Pure and Applied Mathematics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1007/s13226-020-0396-6
Publication status	Published - 1 Mar 2020

Keywords

Abel differential equation
Polynomial differential equation
Riccati differential equation
linear differential equation
polynomial solution

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10.1007/s13226-020-0396-6

https://ddd.uab.cat/record/221356

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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",

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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

U2 - 10.1007/s13226-020-0396-6

DO - 10.1007/s13226-020-0396-6

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AN - SCOPUS:85081719192

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EP - 232

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

IS - 1

ER -

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

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Keywords

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