On first integrals for polynomial differential equations on the line
Volume 107 / 1993
Studia Mathematica 107 (1993), 205-211
DOI: 10.4064/sm-107-2-205-211
Abstract
We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.
