Rational Solutions of Parametric First-Order Algebraic Differential Equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908441112477696 |
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| author | Falkensteiner, Sebastian Sendra, Rafael |
| author_facet | Falkensteiner, Sebastian Sendra, Rafael |
| contents | In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the existence of rational solutions of the differential equation, with parametric coefficients, when the parameters are specialized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05102 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational Solutions of Parametric First-Order Algebraic Differential Equations Falkensteiner, Sebastian Sendra, Rafael Symbolic Computation 34A05, 14H50, 34A34, 30C15, 35B30 In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the existence of rational solutions of the differential equation, with parametric coefficients, when the parameters are specialized. |
| title | Rational Solutions of Parametric First-Order Algebraic Differential Equations |
| topic | Symbolic Computation 34A05, 14H50, 34A34, 30C15, 35B30 |
| url | https://arxiv.org/abs/2307.05102 |