Discovering Solutions to Ordinary Differential Equations

Mike Mezzino
University of Houston at Clear Lake

ODE.m, a new differential equations package for Mathematica, greatly enhances Mathematica's differential equation solvers and makes them easier to use. Using Mathematica's comprehensive programming language to systematically apply transformations, ODE.m is able to discover symbolic solutions to some nonlinear differential equations for which only numerical solutions are presently available. In addition, the user can optionally specify that the method of solution and plotting solutions has been simplified.  Both numerical and "seminumerical" approximations are included. The design and internal structure of the principal commands in this package will also be discussed.