Solution

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

For
$$
\dot x=y+h(r^2)x,\qquad
\dot y=-x+h(r^2)y,
\qquad r^2=x^2+y^2,
$$
polar coordinates give
$$
\dot r=h(r^2)r,\qquad \dot\theta=-1.
$$
The trajectories rotate clockwise, while the sign of the radial equation determines stability.


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