O.D.E Integrating Factor Help

Question

I've been doing alright so far, but I can't seem to find the special integrating factor for this question, and Wolfram, as well as Symbolab, are unable to help. Please let me know:

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

Answer 1

The integrating factor is $1/(xy^2).$ If you multiply through by that, the equation becomes exact.

To find this factor, assume an integrating factor of the form $\mu(xy).$

Answer 2

$$(2x^2y + x)dy + (xy^2 + y)dx = 0$$ Rearrange terms: $$dxy+2x^2ydy + xy^2 dx = 0$$ $$dxy+(xy)(2xdy + y dx )= 0$$ Divide by $(xy)^2$ $$\dfrac {d(xy)}{(xy)^2}+\left(2\dfrac {dy}y + \dfrac { dx}x \right )= 0$$ Integrate. $$\dfrac 1{xy}-\ln |xy^2|=C$$