Mathematics & Science Learning Center
Computer Laboratory

Applications of Differential Equations

Compartmental Analysis

More Examples in Mathematica

(continued from last page...)

Your results should have been very similar to the following:

1. y(0) = 1200

   
   

2. y(0) = 1000

   
   

3. y(0) = 800

   
   

4. y(0) = 600

   
   

5. y(0) = 400

   
   

Notice that in every single case, regardless of initial condition, in the long term the amount of salt in the tank approaches exactly the same value—800 pounds. If you think about our explanation for the asymptotic behavior we witnessed in the original example, you should agree that the same asymptotic behavior should be expected regardless of the initial condition. If you start with more than 800 pounds, the amount in the tank will decrease towards the asymptote, y = 800. If you start with less than 800 pounds, the amount in the tank will increase towards the asymptote, y = 800. If you start with exactly 800 pounds of salt in the tank then this level is maintained, since the concentration in the tank to start with is exactly the same as the concentration of the inflow, i.e. 2 pounds of salt per gallon.

As our grand finale for this sequence of linked examples, use the Show command to display all six of the solutions—mix1 through mix6 on the same graph. Use a PlotRange->All option while you're at it. Come back here when you're done.

Let's go and see what you should have gotten...

If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.