Integrating Factor Method and Absolute Value Bars

[manenbu]

So there's this equation:
$$x^2 y^2 dx + (x^3y-1)dy$$
It has to be solved with the integrating factor method, so I get this:
$$\mu(y) = e^{\int \frac{dy}{y}} = e^{\ln{|y|}} = |y|$$

My question is, what do I do with the absolute value bars?
If I just drop them and multiply the entire equation with y, then I can solve the equation and get:
$$2x^3 y^3 - 3 y^2 = C$$
Which is the correct answer.
But I'm not sure that dropping it will always be correct, so what should be done here?

 

[trambolin]

what is $\ln(-1)$?

 

[manenbu]

It's undefined, and I know that.
This is the reason you put the bars in the first place, but my question was about the integrating factor itself, should it be y or |y|.

 

[HallsofIvy]

Use either y or -y. Since you are multiplying the entire equation by that, it doesn't affect the result.

 

[manenbu]

ok I understand!