Solution (source code)

= Solution

The constant $u=1/(3M)$ satisfies $u=3Mu^2$. It is the circular photon orbit at \b[$r=3M$], the <photon sphere>. A perturbation $u=u_c+\eta$ satisfies $\eta''=\eta$ to first order, so perturbations grow exponentially with orbital angle: the circular null orbit is unstable. Substitution into the <first integral> gives $E^2/L^2=1/(27M^2)$.