A universal differential equation of degree 6
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 \[ \begin{multlined} 4(1+ i\sqrt 3) {y'}^3 {y'''}^2 y''''- 3(1+ i\sqrt 3) {y'}^3 y'' {y''''}^2+ 2(9+ i\sqrt 3) {y'}^2 {y''}^2 y''''- 24{y'}^2 y'' {y'''}^3-\\ 7(1+ i\sqrt 3) y' {y''}^3 {y'''}^2+ 4(3+ i\sqrt 3) {y''}^5 y'''= 0.\end{multlined} \] .
scientific article; zbMATH DE number 1449222