
Solving Initial Value Problems with Mathematica's Solver
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 allpurpose 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 standalone 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.
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