 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-3/3b/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The data are rotationally symmetric, so seek a radial solution. The radial Laplacian in two dimensions gives

\frac{1}{r} (r u^{'})^{'} = 16 r^{2} .

Twice integrating,

u (r) = r^{4} + C lo g r + D .

Regularity at the center forces

C = 0

, and

u (1) = 1

gives

D = 0

. Thus

u (r) = r^{4} .

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