A: dy/dx=(1+y2)/(1+x2) separates as dy/(1+y2)=dx/(1+x2), so variable separable (III). B: x2(dy/dx)=x2−2y2+xy has all terms of degree 2, homogeneous (IV). C: sinx+y=cos(x+y) contains no derivative, not a differential equation (I). D: (x+y)(dy/dx)=1 rewrites as dx/dy=x+y, linear first order in x (II).