separable differential equation

I can't seem to get the solution in my text book, the problem is:

I began by reorganizing to:

expanding the y term and integrating:

giving the following:

where K is the combined constant of integration from both sides

now when I take the exponential, I think I have to raise e to the entire

right side and that I can't do it term by term which simplifies to a division

using log properties and then canceling out the e and ln

now I was thinking I could drop all the absolute values if I throw a +\-

in front of the remaining exponential, so we'll say

solving for y yields:

however my textbook gives:

Please let me know if you can see my mistake, thanks