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...
| Authors: | ; |
|---|---|
| Format: | Article |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:221356 |
| Online Access: | https://ddd.uab.cat/record/221356 https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6 |
| Access Level: | Open access |
| Keyword: | Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation |
| _version_ | 1878742728177614849 |
|---|---|
| author | Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004 |
| author2 | Llibre, Jaume|||0000-0002-9511-5999 |
| author2_role | author |
| author_browse | Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004 Llibre, Jaume|||0000-0002-9511-5999 |
| author_facet | Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004 Llibre, Jaume|||0000-0002-9511-5999 |
| author_role | author |
| collection | Dipòsit Digital de Documents de la UAB |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_fb3282e72c0a7f5caf2f8dfeb4e472c1 |
| institution | Universitat Autònoma de Barcelona |
| instname_str | Universitat Autònoma de Barcelona |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ddd.uab.cat:221356 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| reponame_str | Dipòsit Digital de Documents de la UAB |
| spelling | 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 Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004 Llibre, Jaume|||0000-0002-9511-5999 Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation 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. https://ddd.uab.cat/record/221356 https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6 |
| spellingShingle | 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 Ferragut Amengual, Antoni Manel|||0000-0002-7420-5004 Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation |
| topic_facet | Polynomial differential equation Polynomial solution Linear differential equation Riccati differential equation Abel differential equation |
| url | https://ddd.uab.cat/record/221356 https://dx.doi.org/urn:doi:10.1007/s13226-020-0396-6 |