 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/13e/a/solution

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

p T = κ T_{xx} .

Decay as

x \to \infty

selects

T (x, p) = f (p) e^{- x p / κ} .

The boundary value gives

f (p) = a (\frac{1}{p} - \frac{1}{p + b}) = \frac{ab}{p ( p + b )},

T (x, p) = \frac{ab}{p ( p + b )} e^{- x p / κ} .

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