 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/28k/b/iii/solution

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

Separating variables in

h^{'} = (h - 1) (λh - μ)

with

h (0) = 0

h (t) = \frac{μ ( 1 - e ^{- (λ - μ) t} )}{λ - μ e ^{- (λ - μ) t}}, λ \neq = μ .

For

λ > μ

this tends to

μ / λ

; for

λ < μ

it tends to one, as expected.

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