Looks like you're right and the book has the + and the – the wrong way round.
Find the general solution of the differential equation.
Using partial fractions.
(1/4 /(y-2) -1/4 /(y+2))dy/dx=1/x
solving for y
The book gives an answer of y=2(1-Kx^4)/(1+kx^4).
I'll be happy if you can confirm either answer.