Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

GeneratedParameters is an option that specifies how parameters generated to represent the results of various symbolic operations should be named.

There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...

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 ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...

DifferentialRoot[lde] represents a function that solves the linear differential equation specified by lde[y, x].