Geodesic
On first integrals for polynomial differential equations on the line
Studia Mathematica, Tome 107 (1993) no. 2, pp. 205-211 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. 
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Henryk Żołądek. On first integrals for polynomial differential equations on the line. Studia Mathematica, Tome 107 (1993) no. 2, pp. 205-211. doi: 10.4064/sm-107-2-205-211

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