 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/37e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

P = wρ

give

\overset{ρ}{˙} = - 3 (1 + w) \frac{a ˙}{a} ρ .

On every interval where

a

\frac{d ρ}{ρ} = - 3 (1 + w) \frac{d a}{a} .

ρ = \frac{3 μ}{8 π} a^{- 3 (1 + w)},

where

μ

is a constant. The same expression extends through a regular turning point by continuity.

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