The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

The hypergeometric functions play a unifying role in mathematical analysis since many important functions, such as the Bessel functions and Legendre functions, are special ...

The general form of a nonlinear second-order ODE is For simplicity, assume that the equation can be solved for the highest-order derivative y^ ′′(x) to give There are a few ...

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004. [A89] Abramov, S. A. "Rational Solutions of Linear ...

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

In order to write the most general Mathematica programs you will sometimes need to find out global information about the setup under which your program is being run. Thus, ...

You can enable logging in two ways. The log file records messages as they occur, building up a detailed record of license activity over a period of time. Logging supports ...

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

When searching for a real simple root of a real valued function, it is possible to take advantage of the special geometry of the problem, where the function crosses the axis ...