 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/14b/c/i/solution

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

Fourier transformation in

x

u_{yy} - k^{2} u = 0.

Imposing the two boundary values gives

u (k, y) = \frac{f ( k ) sinh ( ∣ k ∣ ( a - y )) + g ( k ) sinh ( ∣ k ∣ y )}{sinh ( ∣ k ∣ a )} .

The value at

k = 0

is understood by continuity.

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