Meromorphic differential equations having all monomials as solutions
type: Item
instance of: scholarly article
title: Meromorphic differential equations having all monomials as solutions
zbMATH Open document ID: 0759.34004
DOI: 10.1007/BF01199013
published in: Archiv der Mathematik
publication date: 1993-02-10T00:00:00Z
review text: In this paper one considers ordinary differential equations with meromorphic coefficients of the form \(F(y(x),y^{(1)}(x),\dots,y^{(r)}(x))=0\), where \(F(Y_ 0,Y_ 1,\dots,Y_ r)\) is a polynomial in the variables \(Y_ 0,\dots,Y_ r\) with coefficients in the field \(\mathbb{C}\{x\}[x^{-1}]\) of convergent Laurent series in \(x\) over \(\mathbb{C}\). It is shown that essentially the only differential equation of this form with the property that each monomial \(x^ n\) (\(n=0,1,2,\dots\)) is a solution, is the equation \(xy\ddot y- x\dot y^ 2+y\dot y=0\).
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 119838
zbMATH Keywords: ordinary differential equations with meromorphic coefficients
zbMATH Keywords: monomial
author: Arno van den Essen
MaRDI profile type: Publication
cites work: Eulerian systems of partial differential equations and the Jacobian conjecture
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description: scientific article; zbMATH DE number 119838