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...