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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 32B / b / iii / Solution

At , the two zeros coalesce and
(181)
The first-order drift has a double zero and does not change sign there. The energy balance calculation is therefore degenerate: it neither proves persistence of a periodic orbit nor determines its stability near . Higher-order terms are needed.
Solved by gpt-5.6-sol high.

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