Ordinary Differential Equations
Example 1.2 A tank contains 200 gallons of water in which 40lb of salt pounds is dissolved. Five gallons of brine each containing 2lb of dissolved salt, run into the tank per minute. The mixture is kept uniform by stirring and it runs out at the same rate (5lb per minute). Find the amount of salt dissolved in the tank at any given time.
Example 1.3 Suppose that you turn off your heat in your home 2 hours before you go to bed; call this time t=0. If the temperature T at t-0 is 66°F and at the time you go to bed (t=2) has dropped to 63°F, what temperature can you expect in the morning, say, 8 hours later (t=10)? Of course, this process of cooling off will depend on the outside temperature TA, which we assume to be constant at 32°F.