General Solutions of the Abel Differential Equations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866918199418683392 |
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| author | Zhao, Ji-Xiang |
| author_facet | Zhao, Ji-Xiang |
| contents | The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind. A novel derivative condition for the general solution of first-kind Abel equation is introduced. Based on this condition, the general solutions to the first-kind Abel equation with a zero free term are obtained, which in turn enables the derivation of the general solutions to the second-kind Abel equation, and meanwhile, a pair of entangled functions is discovered. These results can be extended to the Lienard equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_10523 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | General Solutions of the Abel Differential Equations Zhao, Ji-Xiang Exactly Solvable and Integrable Systems 34A34, 34A05, 34A25 The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind. A novel derivative condition for the general solution of first-kind Abel equation is introduced. Based on this condition, the general solutions to the first-kind Abel equation with a zero free term are obtained, which in turn enables the derivation of the general solutions to the second-kind Abel equation, and meanwhile, a pair of entangled functions is discovered. These results can be extended to the Lienard equation. |
| title | General Solutions of the Abel Differential Equations |
| topic | Exactly Solvable and Integrable Systems 34A34, 34A05, 34A25 |
| url | https://arxiv.org/abs/2011.10523 |