gDavidov, I agree.
But I just skipped showing a few steps. v^2/2 = GM/(D-x) + C1
I just ignored C for the moment as it's not important I solve for it here: v = √(2GM/(D-x)) + C2
plugging in initial conditions, x=0, v=0, C2 = -√(2GM/D)
And to D H
I've been trying to make sense of what you said...