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Rational Solutions of Parametric First-Order Algebraic Differential Equations

Symbolic Computation 2025-07-10 v3
Authors: Sebastian Falkensteiner , Rafael Sendra
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Abstract

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.

Keywords

first-order logic computer algebra computational complexity

Cite

@article{arxiv.2307.05102,
  title  = {Rational Solutions of Parametric First-Order Algebraic Differential Equations},
  author = {Sebastian Falkensteiner and Rafael Sendra},
  journal= {arXiv preprint arXiv:2307.05102},
  year   = {2025}
}

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