An empty building's temperature on a cold morning drops to 48 degree at 1: 00 a. m. at that time the furnace is turned on with the thermostat set at 66 degree. the time constant for the building is 2 hours and for the building along with its heating system is 1/4 hour. assuming that the outside temperature varies as a cosine wave with a maximum 54 degree at 1: 00 p. m. and a minimum of 27 degree at 1: 00 a. m., set up the initial value problem (with initial condition) that describes this problem. do not solve this ivp.