Model of Temperature Variation inside a Building
The interior temperature of a building changes with the weather outside. Suppose the initial temperature is and that varies between in Fahrenheit degrees with a frequency . Using Newton’s law of cooling, it is possible to write a differential equation for the temperature as a function of time, measured in days, choosing an initial value . The plot of the solution over a range of temperatures is shown, as well as the direction field. Notice that the temperature tends to stabilize after several days.
The differential equation is ( is a constant)
with the analytical solution
 J. R. Brannan and W. E. Boyce, Differential Equations, An Introduction to Modern Methods and Applications, 2nd ed., Hoboken, NJ: John Wiley & Sons, 2011 pp. 11–13.