The basic Maple command for solving differential equations is
`dsolve`. This command can be used to obtain analytical
solutions of linear equations as well as numerical solutions of
nonlinear equations. The basic syntax of the `dsolve` command
for a single linear equation is

> dsolve({deq, initcond},func);

where `deq` represents a differential equation,
`initcond` stands for one or more initial conditions, and
`func` is the function representing the solution of the
differential equation.

Several other Maple commands will be useful to us, including the
`diff` command for computing derivatives, the `subs`
command for substituting sets of parameter values into differential
equations and their soloutions, and several commands from the
`DEtools` package for plotting slope fields and phase
portraits.

This document provides examples of for all of these commands. It
begins with examples of solving linear first and second order
differential equations and then goes on to describe the plotting commands from
the `DEtools` package. Finally, using the dsolve command to
obtain numerical solutions of nonlinear differential equations is
described.

Thu Oct 24 13:25:12 EDT 1996