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Mathematics & Science Learning Center
Computer Laboratory


Slope Fields with Mathematica

Making Slope Fields by Yourself

Using these skills we have just discussed so far, you should now be able to create slope fields for arbitrary differential equations on arbitrary rectangular regions in the plane. In fact that's what we're about to start having you do.

Instructions for the Exercises

Each of the following exercises requires you to create a slope field using Mathematica for a given differential equation, on a given region. Your job will be to:

  1. Switch applications from your browser over to Mathematica
  2. Enter the VectorPlot command, using the correct slope function, all vectors of equal length, with the bounds indicated, the indicated arrow-head status, and the indicated number of vectors
  3. Look at the resulting picture carefully, making sure you understand what is going on with the slopes and why
  4. Switch applications from Mathematica back to your browser
  5. Compare your results with the answers provided to make sure you did the problem correctly

You may wish to save a copy of your notebook when you're finished so that you can use it to study for upcoming exams. If you get lost, or forget what you're supposed to do next, come back here to review the instructions, i.e. switch back to your browser.

Now, choose the type of exercise you wish to work on from the list below. I suggest you simply work through the list in order unless this isn't your first time here, (i.e. unless you're starting back into the exercises after an interruption, or you're reworking some of the exercises for practice.)


  1. Equations of the Form: dy/dx = g(x)
  2. Equations of the Form: dy/dx = g(y)
  3. Equations of the Form: dy/dx = g(x, y)

You are at last finished with this laboratory assignment. Remember that there will be a lab exam covering this material. If you feel that you need the practice you are welcome to start over if you wish. You may also go back to the ODE Laboratories Home Page if you want to get to other laboratory assignments, etc.

Compass 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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