In Problems $1-6,$ identify the equation as separable, linear, exact, or having an integrating factor that is a function of either $x$ alone or $y$ alone.

$(2x+y{x}^{-1})dx+(xy-1)dy=0$

$(2y^3+2y^2)dx+(3y^{2}x+2xy)dy=0$

$(2x+y)dx+(x-2y)dy=0$

$(y^2+2xy)dx-x^{2}dy=0$

$(x^{2}sinx+4y)dx+xdy=0$

$(2y^{2}x-y)dx+xdy=0$ Only $2$ and $6$