# A Universal Ordinary Differential Equation

@article{Bournez2017AUO, title={A Universal Ordinary Differential Equation}, author={O. Bournez and A. Pouly}, journal={ArXiv}, year={2017}, volume={abs/1702.08328} }

An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive continuous function $\epsilon(t)$, it has a $\mathcal{C}^\infty$ solution with $| y(t) - \varphi(t) | < \epsilon(t)$ for all $t$. Lee A. Rubel provided an explicit example of such a polynomial DAE. Other examples of universal DAE have later been… CONTINUE READING

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