 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/10a/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The angular Laplacian sends

sin θ

cos (2 θ) / sin θ

, while

1/ r

is radially harmonic. Therefore

u = \frac{sin θ}{r} .

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