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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.

William W. Farr
Thu Oct 24 13:25:12 EDT 1996