A universal differential equation
- Published in 1981
- Added on
In the collections
There exists a non trivial fourth-order algebraic differential equation \[P(y',y'',y''',y'''') = 0,\] where \(P\) is a polynomial in four variables, with integer coefficients, such that for any continuous function \(\phi\) on \((-\infty,\infty)\) and for any positive continuous function \(\varepsilon(t)\) on \((-\infty,\infty)\), there exists a \(C^{\infty}\) solution \(y\) of \(P=0\) such that \[|y(t)-\phi(t)| \lt \varepsilon(t)\) \forall t \in (-\infty,\infty)\]
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- key
- Auniversaldifferentialequation
- type
- article
- date_added
- 2019-05-09
- date_published
- 1981-09-30
BibTeX entry
@article{Auniversaldifferentialequation, key = {Auniversaldifferentialequation}, type = {article}, title = {A universal differential equation}, author = {Lee A. Rubel}, abstract = {There exists a non trivial fourth-order algebraic differential equation \[P(y',y'',y''',y'''') = 0,\] where \(P\) is a polynomial in four variables, with integer coefficients, such that for any continuous function \(\phi\) on \((-\infty,\infty)\) and for any positive continuous function \(\varepsilon(t)\) on \((-\infty,\infty)\), there exists a \(C^{\{}\infty{\}}\) solution \(y\) of \(P=0\) such that \[|y(t)-\phi(t)| \lt \varepsilon(t)\) \forall t \in (-\infty,\infty)\]}, comment = {}, date_added = {2019-05-09}, date_published = {1981-09-30}, urls = {https://projecteuclid.org/euclid.bams/1183548125}, collections = {Fun maths facts,Unusual computers}, url = {https://projecteuclid.org/euclid.bams/1183548125}, year = 1981, urldate = {2019-05-09} }