 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/6e/b/solution

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

Put

n (a, t) = A (a) T (t)

. Separation gives

\frac{T ^{'}}{T} = - \frac{A ^{'}}{A} - d (a) = r

for a constant

r

. Hence

T (t) = T_{0} e^{r t}, A (a) = A_{0} exp (- r a - \int_{0}^{a} d (s) d s) .

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