Алгебраические овалы и рациональные интегралы систем типа Дарбу

We consider the question of the existence of algebraic solutions, polynomial and rational integrals for systems of ordinary differential equations of the form $\dot x=x+P_n(x,y),\ \dot y=y+Q_n(x,y)$, where $P_n(x,y), $ $Q_n(x,y)$ are homogeneous polynomials of $n$th degree.