Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 105 / 1 / e / Solution

For ${\psi }_0=(r^2+z^2)/2$,The prescribed function is $g=\sqrt{D}$, so part c gives $u_z=-z$. Hence the non-characteristic condition reduces toThe Cauchy-Kovalevskaya theorem therefore guarantees a unique local real-analytic solution at exactly those pointsfor which

Solved by gpt-5.6-sol high.