The transvectants and the integrals for Darboux systems of differential equations

V. Baltag ; I. Calin

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 4-18.

Résumé

We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems $dx/dt=P{1}_{(}x,y)+xC(x,y)$, $dy/dt=Q{1}_{(}x,y)+yC(x,y)$, where real homogeneous polynomials $P_1$ and $Q_1$ have the first degree and $C(x,y)$ is a real homogeneous polynomial of degree $r\ge 1$. 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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