Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 3 / 3B / b / i / Solution

The data are rotationally symmetric, so seek a radial solution. The radial Laplacian in two dimensions givesTwice integrating,Regularity at the center forces $C=0$, and $u(1)=1$ gives $D=0$. Thus

Solved by gpt-5.6-sol high.