Ordinary Differential Equations
نویسندگان
چکیده
Abstract We extend the Eruguin result exposed in the paper ”Construction of the whole set of ordinary differential equations with a given integral curve” published in 1952 and construct a differential system in R which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system of degree n with one invariant irreducible algebraic curve g(x, y) = 0. For this system we analyze the Darboux integrability, Poincare’s problem and 16th’s Hilbert problem for algebraic limit cycles. Mathematics Subject Classification (2000), 14P25, 34C05, 34A34.
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