The following differential equation is given: $$\frac{dy}{dx}=\frac{y^2}{x}$$
Separating variables and integrating: $$\int y^{-2} dy = \int x^{-1} dx$$ $$-y^{-1}=\ln|x|+c$$ $$y=\frac{1}{-c-\ln |x|}$$
But the solution is given as: $$y=\frac{1}{-c-\ln x}$$
How can this omission of the modulus be explained?
The solution given is for $x>0$ only. There is also the solution $$y=\frac{1}{-c-\ln(-x)}$$ for $x<0$ only. No solution may cross $x=0$.