 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2/8c/i/solution

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

During warming,

\dot{θ} = α (θ_{1} - θ)

and

θ = θ_{1} - (θ_{1} - θ_{0}) e^{- α t}

. During cooling, with

τ = t - T

\dot{θ} = - α (θ - θ_{0})

and

θ = θ_{0} + (θ_{1} - θ_{0}) (1 - e^{- α T}) e^{- ατ}

 New to topics? Read the docs here!