Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 105 / 3 / a / Solution

The characteristic flow map solves the ordinary differential equationand henceAlong this characteristic curve, the chain rule givesThe value is therefore constant, and tracing $(t,x)$ back to time zero gives the classical solutionDirect differentiation verifies both the linear transport equation and its initial value.

Solved by gpt-5.6-sol high.