Rational solutions of parametric first-order algebraic differential equations
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.
Authors
- Sebastian Falkensteiner (ORCID: https://orcid.org/0000-0001-8701-5317)
- Juana Sendra (ORCID: https://orcid.org/0000-0002-9927-169X)
Institutions
- Max Planck Institute for Mathematics in the Sciences (DE)
- Max Planck Institute for Mathematics (DE)
- Institute of Mathematical Sciences (ES)
Publication Details
- Journal
- Bulletin des Sciences Mathématiques
- Published
- 2025-06-27
- DOI
- https://doi.org/10.1016/j.bulsci.2025.103694
- Citations
- 1
- Primary Topic
- Numerical methods for differential equations
- Type
- article
- Field-Weighted Citation Impact
- 2.63
Funders
- Ministerio de Ciencia, Innovación y Universidades
- Österreichische Agentur für Internationale Mobilität und Kooperation in Bildung, Wissenschaft und Forschung
- Agencia Estatal de Investigación