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IMI/Publicaţii/BASM/Ediţii/BASM n.1 (56), 2008/

The transvectants and the integrals for Darboux systems of differential equations.

Authors: Baltag Valeriu, Calin Iurie

Abstract

We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems dx/dt=P1(x,y)+xC(x,y), dy/dt=Q1(x,y)+yC(x,y), where real homogeneous polynomials P1 and Q1 have the first degree and C(x,y) is a real homogeneous polynomial of degree r≥1. In generic cases the invariant algebraic curves and the first integrals for these systems are constructed. The constructed invariant algebraic curves are expressed by comitants and invariants of investigated systems.

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