Goals of This Document

The design of DSolve is modular: the algorithms for different classes of problems work independently of one other. Once a problem has been classified (as described in the previous section), the available methods for that class are tried in a specific sequence until a solution is obtained. The code has a hierarchical structure whereby the solution of complex problems is reduced to the solution of relatively simpler problems, for which a greater variety of methods is available. For example, higher-order ODEs are typically solved by reducing their order to 1 or 2.

The process described is done internally and does not require any intervention from the user. For this reason, this document has the following basic goals.

To provide enough information and tips so that users can pose problems to DSolve in the most appropriate form and apply the solutions in their work. This is accomplished through a substantial number of examples. A summary of this information is given in the section Working with DSolve.

To give a catalog of the kinds of problems that can be handled by DSolve as well as the nature of the solutions for each case. This is provided in the sections on ODEs, PDEs, DAEs, and boundary value problems (BVPs).

The author hopes that this document will be useful in acquiring a basic knowledge of DSolve and also serve as a ready reference for information on more advanced topics.