## Applications of Differential Equations

### Solving The Example in Mathematica

(continued from last page...)

For easy reference, I'll repeat the important details from the last page.

### The Example

A large tank initially holds 400 gallons of water into which 1600 pounds of a certain salt has been dissolved. An inflow pipe brings in water containing 2 pounds of the same salt per gallon at a rate of 5 gallons per minute. An outflow pipe allows the fully mixed fluid in the tank to exit at the same rate of 5 gallons per minute. Find the initial value problem that models the amount of the salt, y, in the tank at time t.

### The Resulting Initial Value Problem

dy/dt = 10 - y/80

y(0) = 1600

By now you've solved enough IVPs with Mathematica for you to be able to solve this particular IVP without me telling you exactly what to type. Solve it now using the DSolve command, reading your result into the variable mix1. Use the [[1,1,2]] trick to strip out the important part of the solution that Mathematica returns to you, and read the result back into mix1 again. Come back here when you're done.

Let's go look at 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.

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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