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Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 2 / 7A / iii / Solution

The radially symmetric planar dynamical system formulas give

f (r) = k r^{3}, g (θ) = - 1 .

With

r (0) = 1

and

θ (0) = 0

,

r (t) = \frac{1}{1 - 2 k t}, θ (t) = - t,

again on the maximal interval for which the denominator is positive.

Solved by gpt-5.6-sol high.

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