 Solution

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

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

Each sine product is a Dirichlet eigenfunction. The squared wave-number sums are

24 π^{2}

and

30 π^{2}

, respectively, so

u = - \frac{sin ( 2 π x ) sin ( 2 π y ) sin ( 4 π z )}{24 π ^{2}} + \frac{sin ( 2 π x ) sin ( π y ) sin ( 5 π z )}{30 π ^{2}} .

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