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 some part...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | Inglês |
| OAI Identifier: | oai:ddd.uab.cat:221356 |
| Acesso em linha: | https://ddd.uab.cat/record/221356 https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation |
| Resumo: | 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. |
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