### A class of integrable polynomial vector fields

We study the integrability of two-dimensional autonomous systems in the plane of the form $=-y+{X}_{s}(x,y)$, $=x+{Y}_{s}(x,y)$, where Xs(x,y) and Ys(x,y) are homogeneous polynomials of degree s with s≥2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable ${({x}^{2}+{y}^{2})}^{s/2-1}$ with coefficients being functions of tan−1(y/x).