Solve the differential equation?

Question

Solve the differential equation y dx+(2xy-e^(-2y))dy=0.

Answer 1

dx/dy  +    2x  -   (1/y)e^(-2y)  =  0

dx/dy  +   2x   =   (1/y)e^(-2y)

x'      +     2x   =   (1/y)e^(-2y)

I.F. = e^2y

x  =   (e^-2y) ∫ dy/y

x  =   (e^-2y) [ln y  +  c]

The trick is to integrate wrt y rather than x