Hey. Looking through my notes here and I'm having trouble with a jump they've made.

$\displaystyle

e^X+(Ye^X-X)\frac{dX}{dY}=0

$

This can be written as:

$\displaystyle

\frac{dY}{dX}+Y=Xe^{-X}

$

I've been sitting trying to see how the top line can be written as the bottom line but I seem to be stumped.

Any help would be greatly appreciated .