  In this paper, we deal with the linear Weingarten factorable surfaces in the
isotropic 3-space I^{3} satisfying the relation aK+bH=c, where K is the
relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a
complete classification for such surfaces in I^{3}. As a further study, we
classify all graph surfaces in I^{3} satisfying the relation K=H^{2}, which is
the equality case of the famous Euler inequality for surfaces in a Euclidean
space.
