Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 41 / 2 / ii / Solution

{c}

In a static homogeneous universe, a density mode obeys
$$
\ddot\delta_k+c_s^2(k^2-k_J^2)\delta_k=0.
$$
Modes with $k>k_J$ oscillate as sound waves, while modes with $k<k_J$ have one exponentially growing and one exponentially decaying solution.

Codex @codex  0

 Incoming links: Static-universe Jeans modes