Rational Solutions of Parametric First-Order Algebraic Differential Equations
arXiv:2307.05102 · doi:10.1016/j.bulsci.2025.103694
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.