with the intial condition that y(1)=1. I tried to separate them and on the left side I have that 1/2y=(lnx)^2 over 2 plus C ... Am I on the right track?
I just went through it in my head, and using u=ln(x) to solve ln(x)/x i got the same as you, but you need to have a negative in there from solving int(y^-2), now you just need to use y(1)=1 to find C.