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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>