Analytic General Solution of the Riccati equation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918433875034112 |
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| author | Ji-Xiang, Zhao |
| author_facet | Ji-Xiang, Zhao |
| contents | A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytic general solution is presented, which can be extended to second-order linear ordinary differential equation. This result may provide valuable mathematical criteria for in-depth research on quantum mechanics, relativity and dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic General Solution of the Riccati equation Ji-Xiang, Zhao Exactly Solvable and Integrable Systems 34A34, 34A25, 34A05 A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytic general solution is presented, which can be extended to second-order linear ordinary differential equation. This result may provide valuable mathematical criteria for in-depth research on quantum mechanics, relativity and dynamical systems. |
| title | Analytic General Solution of the Riccati equation |
| topic | Exactly Solvable and Integrable Systems 34A34, 34A25, 34A05 |
| url | https://arxiv.org/abs/2510.19297 |