 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-4/6c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Again put

x = 1 + u

. Then

u^{'} (t) = α (1 + u (t - T)) (- u (t)) = - αu (t) - αu (t - T) u (t) .

u^{'} = - αu,

whose sole characteristic exponent is

- α < 0

and is independent of

T

x (t) = 1 is locally asymptotically stable for every T \geq 0.

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