A+ CATEGORY SCIENTIFIC UNIT

On first integrals for polynomial differential equations on the line

Volume 107 / 1993

Henryk Żołądek 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.

Authors

  • Henryk Żołądek

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