Thank you very much.
I think in your solution one of the y's turned into an x.
The final answer is (by the book) (y - 2e^(2x))/(2e^(2y) - x).
Also: could you explain exactly how you got the "2(dy/dx)e^(2y)" bit in your first line.
I know it is differentiating implicitly and you have to do something with ln but I am not sure how it goes.