Solving Initial Value Problems with Mathematica's Solver

(continued from last page...)

Final Note: At this point we've pretty much completed our exploration of Mathematica's standard solver routines. (Though we still haven't tried out genuine systems of differential equations—those come much later.) It must be emphasized that the differential equation solver in Mathematica is not the best one available. There are dedicated differential equation solvers that can do a better job (i.e. they can solve some of those problems where Mathematica just draws a blank.) Remember, Mathematica is designed to be an all-purpose system—it can do an enormous variety of mathematics. Necessarily its ability in certain specialized applications can be a bit stunted in comparison to a stand-alone program. However, one of Mathematica's other features is its extensibility, i.e. it is programmable—new features can be added to it by the user. These are called packages, and if we get time we'll eventually look at some Mathematica packages written specifically for solving some of the types of differential equations that the built in solver cannot do.

You are at last finished with this laboratory assignment. Remember that there will be a lab exam covering this material. If you feel that you need the practice you are welcome to start over if you wish. You may also go back to the ODE Laboratories Home Page if you want to get to other laboratory assignments, etc.