Visualizing Differential Equations with the VisualDSolve Package

Antonín Slavík, Charles University in Prague, Czech Republic

Stan Wagon, Macalester College, St. Paul, Minnesota

Abstract

The VisualDSolve package was written by Dan Schwalbe and Stan Wagon in 1994 and was originally accompanied by a printed book containing documentation and many examples of differential equations modeling suitable for a university course. The package provided a wide variety of tools for visualizing solutions of ordinary differential equations, including commands to generate isoclines, vector fields, flow fields, shaded phase-plane images, and Poincaré sections. 

We have recently updated the package and examples to be compatible with Mathematica 7, using the new features such as dynamic demonstrations, the RegionPlot function, parallel computation, and more. The package includes improved documentation in the form of an electronic book with numerous new examples and one completely new chapter with some unusual applications. The following image presents a sampling of the graphics capabilities of the VisualDSolve package.