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