Initial conditions of ODEs: Why is $\frac{}{} = \frac{1}{ \cdot ()}$?

Question

I've started reading this paper (kindly check out the paper for more context, figure 1 provides a visualization of the problem) where it describes light trajectories on a Schwarzschild spacetime and stumbled upon the following formula:
$$\frac{}{} = \frac{1}{ \cdot ()}$$
Where $ = \frac{1}{}$, both $u$ and $\frac{}{}$ are the initial conditions of the second order differential orbital equation of the photon.
My question is why is that $\frac{du}{d\phi} = \frac{1}{D \cdot tan(\alpha)}$? Is there any intuition behind the formulation of this initial condition? And can it be geometrically or analytically proven? I've asked this question on physics stack exchange and got no answer at all.