 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/2/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

w^{''} = 0

satisfying

w (0) = 0

and

k w^{'} (L) = H

. Hence

w (x) = H x / k

. Subtracting it gives the homogeneous problem

v_{t} = ν v_{xx}, v (0, t) = 0, v_{x} (L, t) = 0, v (x, 0) = - \frac{H x}{k} .

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