 Solution

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

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

Put

Δ = T_{0} - T_{\infty}

. Before either forcing term acts, Newton's law of cooling gives

T_{1} (t) = T_{\infty} + Δ e^{- a t} (0 < t \leq 1), T_{2} (t) = T_{\infty} + Δ e^{- a t} (t > 0) .

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