 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/8/ii/solution

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

Within this polynomial family,

u (0, 0) = 0

already holds and

u (1, 0) = 1 + β = 0

gives

β = - 1

. Thus one solution is

u (x, t) = x^{2} - x + t .

Two specified point values alone do not give uniqueness among all solutions of the heat equation.

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