A Classification of First Order Differential Equations

2023/02/12 by Kumbhakar, Partha, Roy, Ursashi, Srinivasan, Varadharaj R. · 2 citations
#12FXX #12H05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.07083

Abstract

Let k be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over k and study the algebraic dependence of solutions of a given first order differential equation. Our results generalize parts of the work of Noordman et al. (MR4378074) and complements the work of Freitag et al. (MR4506775).

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