 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/14e/c/solution

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

Multiplying

D n'' + f (n) = 0

n'

and using the endpoint conditions gives the logistic front

n_{0} (x) = \frac{1}{1 + e ^{x / 2 D}} .

It has

n_{0} (0) = 1/2

and direct differentiation verifies the equation for

r = 1/2

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