Integrating Factor Proof: Combining Equations for Exact First-Order ODEs

[physicsjock]

Hey,

I've just been following this proof for a integrating factor of (xy),

http://mathworld.wolfram.com/ExactFirst-OrderOrdinaryDifferentialEquation.html

it starts at at equation (22)

I understood it all a few days ago and now I seem to have forgotten this one step.

It says after eq(22) and (23)

"Combining these two" gives (24)

What does it mean by combining the two?

dividing the top equation by the second?

If that's the case how come dg/dx = dg/dy ?

Thanks in advance

 

[tiny-tim]

hey physicsjock!

(22) and (23) are badly written

they should say:

∂µ/∂x = ∂g/∂(xy) y

∂µ/∂y = ∂g/∂(xy) x​

don't ever write like that!