Getting rid of the absolute value in the resolution of a differential equation

62 Views Asked by At

I have this differential equation as an exercise:

$y' = y^2 - uy$, where u is a real parameter.

While trying to resolve it, I got to a point where I have:

$|\frac{y-u}{y}| = Ce^{ux}$, where $C$ is a positive real number.

Can I discard the absolute value if I extend the domain of $C$ to any non-zero real number? Am I leaving some solutions out by doing so?