Mathematics & Science
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Solving the Preliminary Example
We're going to use Mathematica to help us verify some solutions to the example we encountered in the introduction to this laboratory, namely:
We said that a solution was:
To verify that they really work as solutions, we simply need to do a little substituting. We need to substitute these values of x(t), and y(t) into both equations, and determine whether we get true statements. Let's start with equation (1):
and let's first address the left hand side. To do the check we need to substitute the proposed value of x(t) into x(t) itself, and then differentiate with respect to t. The following command does this in a single step:
Let's now launch Mathematica, and give the command a try.
You can switch to Mathematica by clicking on the button at left. This will open up a fresh notebook for you. Remember that it will take it a while to start up! Don't forget to come back here when you're done! See you in a few minutes.
Now let's go see what you should have gotten...
ODE Laboratories: A Sabbatical Project by Christopher A. Barker
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