Аннотация:
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 $P_1$ 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.
Ключевые слова и фразы:Polynomial differential systems, Darboux integrability, first integrals, invariant algebraic curve, invariant, comitant, transvectant.