 ## Solving "Impossible" Differential Equations with Mathematica

Use NDSolve to work the initial value problems listed below in the exercises. For each problem you should complete the following three tasks:

• Solve the initial value problem on the specified x-domain, assigning the first solution to sola, the next to solb, the next to solc, and so on. (Ignore any warnings about spelling errors.)

• Evaluate the solution at the specified values of x.

• Plot the graph of the solution over the specified x-domain.

### Exercises

Here they are! Don't forget to do all three of the tasks listed above to each exercise. Remember, you can flip between Mathematica and your browser if you need to check on the details of a problem.

1. y″ + (1 + (y′ )2)1/2 = 0, y(0) = 1, y′(0) = 0, on -3 ≤ x ≤ 3.

Evaluate at x = -2, 0, 2.

2. y″ + sin y = 0, y(0) = 0, y′(0) = 2, on 0 ≤ x ≤ 10.

Evaluate at x = π, 4, 5π/2, 9.999. (Use N to get proper decimal answers.)

3. y′ = sin(xy), y(0) = 1, on 0 ≤ x ≤ 10.

Evaluate at x = 2, 4, 8.

4. y″ + (1/2)y′ + sin y = 0, y(0) = 1, y′(0) = 1, on 0 ≤ x ≤ 14.

Evaluate at x = 2, 4, 8.

Go to Mathematica now and do the problems. Come back here when you're done. Click on the button provided on the left to switch to a fresh Mathematica document with the form of these problems already entered for you. Come back here to your browser when you are finished. Welcome back! You may be wondering how well you did. Click on the icon on the left to see the answers you should have gotten. (Only the answers are given, so if you don't match our results you need to figure out what you did wrong.)

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. 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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