%-*-EMaxima-*-
Maxima has many abilities beyond those of basic calculus.  Here we will examine
its ability to solve certain classes of ordinary differential equations.

\section{Ordinary Differential Equations}

We'll start things off with a basic example.  Suppose we wish to solve the
basic first-order separable differential equation $$dy/dx=y^3*\sin(x)$$

\beginmaximasession
load(ode2)$
odeeqn1 : 'diff(y,x) = y^3*sin(x);
ode(odeeqn1,y,x);
\maximatexsession
\C1.  load(ode2); \\
\p  \\
\D\endmaximasession

This of course is a trivial equation, which can be checked using separation of
variables, but it illustrates several properties of the ode solver.  First and
most important, any expression like \texttt{diff} needs the \texttt{'} 
character in front of it, to prevent Maxima from trying to evaluate it.  
Another feature to note is the importance of the order of the variables in the \texttt{ode} command.  \texttt{y} is the dependant variable, \texttt{x} the 
independant.  
