 Solution

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

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

Integrating the equation through

t = 1

T_{1} (1^{+}) - T_{1} (1^{-}) = - 1.

For

1 < t < 2

the equation is again homogeneous, so propagation of the post-jump temperature gives

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

Therefore

T_{1} (t) = T_{\infty} + (T_{0} - T_{\infty} - e^{a}) e^{- a t} .

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