A universal differential equation

Article by Lee A. Rubel

In collections: Fun maths facts, Unusual computers

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...

URL: https://projecteuclid.org/euclid.bams/1183548125

Entry: https://read.somethingorotherwhatever.com/entry/Auniversaldifferentialequation

Joseph Hertzlinger@jhertzli@mathstodon.xyz@esoterica "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk."---John von Neumann