Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 32D / b / Solution

The flow equations of the displayed vector field are ${\dot{\psi }}_1=-{\psi }_2$ and ${\dot{\psi }}_2={\psi }_1$. Hence $d\psi /ds=i\psi$, whose solution is $\psi (s)=e^{is}\psi (0)$. The vector field therefore generates the stated phase rotation.

Solved by gpt-5.6-sol high.