 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-3/37b/a/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Write

y = y_{0} + Δ y, y_{0} = \frac{s i n ϕ}{b},

where

Δ y

is first order in

M

. Substitution into

y^{''} + y = 3 M y^{2}

and omission of terms of order

M Δ y

and

(Δ y)^{2}

gives

Δ y^{''} + Δ y = 3 M y_{0}^{2} = \frac{3 M}{2 b ^{2}} (1 - cos 2 ϕ) .

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