Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give ...

This gives a result for the integral of x^n that is valid for almost all values of n. For the special case of x^-1, however, the correct result is different. The overall goal ...

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...

CreateIntermediateDirectories is an option for CreateDirectory and related functions that specifies whether to create intermediate directories in a directory path specified.

Path is an option for Get and related functions which gives a list of directories to search in attempting to find an external file.

$Failed is a special symbol returned by certain functions when they cannot do what they were asked to do.

DirectedInfinity[] represents an infinite numerical quantity whose direction in the complex plane is unknown. DirectedInfinity[z] represents an infinite numerical quantity ...

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 ...

Mathematica is uniquely suited for processing symbolic expressions because of its powerful pattern-matching abilities and large collection of built-in structural manipulation ...

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...