A universal differential equation of degree 6
type: Item
instance of: scholarly article
title: A universal differential equation of degree 6
zbMATH Open document ID: 0963.34003
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-14T00:00:00Z
review text: The author demonstrates the following theorem: There exists a nontrivial fourth-order algebraic differential equation such that any real continuous function on the real axis can be uniformly approximated by the imaginary parts of the complex-valued \(\mathbb{C}^\infty\)-solutions to this algebraic differential equation. One such specific algebraic differential equation is \[ \begin{multlined} 4(1+ i\sqrt 3) {y'}^3 {y'''}^2 y''''- 3(1+ i\sqrt 3) {y'}^3 y'' {y''''}^2+ 2(9+ i\sqrt 3) {y'}^2 {y''}^2 y''''- 24{y'}^2 y'' {y'''}^3-\\ 7(1+ i\sqrt 3) y' {y''}^3 {y'''}^2+ 4(3+ i\sqrt 3) {y''}^5 y'''= 0.\end{multlined} \] .
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 1449222
zbMATH Keywords: algebraic differential equation
zbMATH Keywords: \(\mathbb{C}^\infty\)-solutions
author: Carsten Elsner
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6730
OpenAlex ID: W2074311814
cites work: Universal formulae and universal differential equations
cites work: On the Approximation of Continuous Functions by C∞‐Solutions of Third‐Order Algebraic Differential Equations
cites work: A universal functional equation
cites work: A universal differential equation
Wikidata QID: Q115395374
DOI: 10.1006/JMAA.2000.6730
description: scientific article; zbMATH DE number 1449222