 ## Solving "Impossible" Differential Equations with Mathematica

(continued from last page...)

Your results should have looked like this:

?InterpolatingFunction Well that was sort of what we expected an approximate function. What Mathematica has basically done to solve our differential equation is produce a list of points that lie "close" to the actual function that solves the initial value problem. Picking the output to pieces:

• domain in the description refers to the domain of x-values that the solution is valid over. Notice that in the actual solution we found on the last page this domain was {0., 5.}, which is the same as the the domain we gave Mathematica in the original NDSolve command.

• table in the description refers to the list of y-values that have been calculated to correspond to the given domain of x-values—the table in our answer was replaced by <> because the actual table was too huge to show. Mathematica kindly interpolates a function through the approximate points for us, i.e. it "joins the dots" as we described earlier.

Now how does one use a solution such as this one? We'll see on the next page... 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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