Mathematics & Science Learning Center
Computer Laboratory

Solving Systems

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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:

• x(t) = e^{- t}
• y(t) = e^3t

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:

D[x[t]/.x[t]->E^(-t),t]

Let's now launch Mathematica, and give the command a try.

Now let's go see what you should have gotten...

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