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

The Cauchy-Kovalevskaya theorem says that an order-$k$ scalar quasilinear partial differential equation with real-analytic coefficients has a unique local real-analytic solution near each point of a real-analytic non-characteristic hypersurface, provided the prescribed Cauchy dataare real analytic there. The uniqueness is among local real-analytic solutions agreeing with all of those data.

Solved by gpt-5.6-sol high.