(Solution) - Heating and cooling of a building can be modeled by the ODE -(2025 Original AI-Free Solution)

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Heating and cooling of a building can be modeled by the ODE T' = k1(T ? Ta) + k2(T ? Tw) + P, where T = T (t) is the temperature in the building at time t, Ta the outside temperature, Tw the temperature wanted in the building, and P the rate of increase of T due to machines and people in the building, and k1 and k2 are (negative) constants. Solve this ODE, assuming P = const, Tw = const, and Ta varying sinusoidally over 24 hours, say Ta = A ? C cos (2?/24)t. Discuss the effect of each term of the equation on the solution.