Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 312 / 4 / d / Solution

The $\ell =2$ projection of the Boltzmann hierarchy isIn tight coupling, ${\Theta }_2=O(k/\Gamma )$ and ${\Theta }_3$ is higher order. Neglecting ${\Theta }_2^{\prime }$ relative to $\Gamma {\Theta }_2$ at leading order givesso $C=2/5$.

Solved by gpt-5.6-sol high.