• Media type: E-Article
  • Title: Rubel's Universal Differential Equation
  • Contributor: Duffin, R. J.
  • imprint: National Academy of Sciences of the United States of America, 1981
  • Published in: Proceedings of the National Academy of Sciences of the United States of America
  • Language: English
  • ISSN: 0027-8424
  • Origination:
  • Footnote:
  • Description: <p>Fourth-order differential equations such as 16y<sup>′ ′ ′ ′</sup>y<sup>′<sup>2</sup> </sup>-32y<sup>′ ′ ′</sup>y<sup>′ ′</sup>y<sup>′</sup>+17y<sup>′ ′<sup>3</sup> </sup>=0 are developed. It is shown that the equation is ``universal'' in the sense that any continuous function can be approximated with arbitrary accuracy over the whole x axis by a solution y(x) of the equation. This solution is a piecewise polynomial of degree 9 and of class C<sup>4</sup>.</p>
  • Access State: Open Access