Universal formulae and universal differential equations
type: Item
instance of: scholarly article
title: Universal formulae and universal differential equations
zbMATH Open document ID: 0622.34012
DOI: 10.2307/1971279
published in: Annals of Mathematics. Second Series
publication date: 1986-01-01T00:00:00Z
review text: By an nth order ADE \(\bar P\) is meant an algebraic differential equation of the form \(\bar P(y)=P(y,y',y'',...,y^{(n)})=0\) where P is a polynomial in \((n+1)\) variables with rational coefficients. The author proves many results including: 1) There exists a nontrivial ADE (order \(\leq 19)\), whose polynomial solutions in Q[x] are dense in C(I), for any compact interval I; 2) a theorem which is essentially a strengthened version of R. C. Buck's result.
reviewed by: N.L.Maria
Mathematics Subject Classification ID: 34A99
zbMATH DE Number: 4008838
zbMATH Keywords: algebraic differential equation
zbMATH Keywords: polynomial solutions
author: Michael Boshernitzan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971279
OpenAlex ID: W2034639332
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description: scientific article; zbMATH DE number 4008838