 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-2/7c/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

For

t > 2

, the Heaviside step function contributes a constant unit forcing. Solving the resulting first-order linear differential equation from the value at

t = 2

gives

T_{1} (t) = T_{\infty} + (Δ - e^{a}) e^{- a t} + \frac{1}{a} (1 - e^{- a (t - 2)}) .

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