its a matlab exercise :

Problem 3: Heat transfer in a house In this problem you will analyze a mathematical model that predicts the temperature in different areas of a home using Newton's Law of Cooling and Heating. A home with a main floor, an attic and a basement is shown below. Attic Main floor Basement The main room's ceiling and walls are insulated. The walls and the floor of the basement are surrounded by the dirt in the ground. The basement ceiling is insulated with the floor of the main floor and a layer of insulation. The roof is lightly insulated. Let - x(t) be the temperature of the basement (in F ) at time in hours. - y(1) be the temperature of the main floor (in "F) at time in hours. - z(t) be the temperature of the attic (in F) at time 1 in hours. Assume the temperature outside the house is 32F and the ground temperature is 40F. The system of differential equation satisfied by these functions is x=0.75(45x)+0.5(yx)y=0.5(yx)+0.2(32y)+0.2(zy)z=0.2(zy)+0.8(32z) Initially the temperatures (at noon) in the basement, the main floor and the attic are 45,659 and 60F respectively. i) Solve the system of differential equations using Matlab (Numerically with ODE45). Plot your solutions for an interval of time long enough to be able to predict if the temperatures in the different sections of the house reach an equilibrium in the long run