Error on Matlab and Wolfram Alpha? I solved the differential equation 
$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{y^2-1}{2y}$, in the following way:
$\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{y^2-1}{2y} <=>$
$\int \frac{2y}{y^{2}-1}dy=\int1dx <=> ln\left| y^2-1\right |=x+C<=>$
$|y^2-1|=e^xe^C <=> \pm (y^2-1)=e^xe^C <=> y^2-1=Ke^x$, for a constant K, such that $K=\pm e^c$
$<=> y^2=Ke^x+1<=> y= \pm \sqrt{Ke^x+1}$
Now Wolfram Alpha(http://www.wolframalpha.com/input/?i=dy%2Fdx%3D%28y%5E2-1%29%2F%282y%29) and Matlab both tell me that the solution to the original equation is:
$\pm \sqrt{e^Ce^x+1}$, meaning that my constant K can only assume positive values. Is my solution wrong or are both of these software wrong?
Thanks in advance.

You are right, except that you should be more careful with the constant solutions $y=\pm 1$. (In the final answer, they correspond to $K=0$, but you have defined $K=\pm e^C$, which can never be zero, so you have to "repair" the solution by including those cases "by hand".)
