Hydrogen radial equation solution's boundary condition for $r \to 0$

Question

I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to the Coloumb potential. My professor stated that the divergence of the effective potential for $r \to 0$ requires that the condition $$u(0)=0$$ must be imposed. I do not understand where this boundary condition comes from.