Solving "Impossible" Differential Equations with Mathematica

We have already had some experience with Mathematica's built in symbolic solver, and have noticed that:

  • it can be a little slow
  • it doesn't always manage to find a solution

The second of these observations comes as no surprise after what we discussed in the introduction. Fortunately, Mathematica has a built in command that numerically solves differential equations—it's called NDSolve. This routine can deal with initial value problems that cannot be solved symbolically. There is also an added bonus! NDSolve is usually faster than DSolve on the same problems.

Let's start off by taking the usual first step. Ask Mathematica for the syntax of NDSolve.

Mathematica LogoYou can switch to Mathematica by clicking on the button at left. This will open up a fresh notebook for you. Don't forget to come back here when you're done! See you in a few minutes.

Welcome back! Let's go see what you should have just gotten...

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