Non-exact differential equation where does not exist integrating factor dependent on x and y only Our calculus professor gave us a few supplementary problems on differential equations and I'm trying to solve the non-exact differential equation 
$$(6y+x^2y^2)+(8x+x^3y)y'=0$$
I tried finding both $\frac{M_y-N_x}{N}$ and $\frac{M_y-N_x}{-M}$, but neither give a function only dependent of x or y only.
Any other way to approach this equation?

$$(6y+x^2y^2)dx+(8x+x^3y)dy=0$$
$$(6ydx+8xdy)+(x^2y^2dx+x^3ydy)=0$$
Divide by $x^2y$:
$$3\dfrac {dx}{x^2}+4\dfrac {dy}{xy}+\dfrac 12d(xy)=0$$
Multiply by $(xy)^4$:
$$3x^2y^4 {dx}+4x^3y^3dy+\dfrac 12(xy)^4d(xy)=0$$
It's exacy now:
$$(y^4 {dx^3}+x^3dy^4)+\dfrac 12(xy)^4d(xy)=0$$
$$d(x^3y^4)+\dfrac 12(xy)^4d(xy)=0$$
Integrate.
$$10x^3y^4+(xy)^5=C$$

So the integrating factor $\mu (x,y)$ depends on both $x$ and $y$ and we have: $$\mu (x,y)=x^2y^3$$
