Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

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 ...

Overview Supported Development Platforms Installing the MathLink Components

BubbleChart[{{x_1, y_1, z_1}, {x_2, y_2, z_2}, ...}] makes a bubble chart with bubbles at positions {x_i, y_i} with sizes z_i.BubbleChart[{..., w_i[{x_i, y_i, z_i}, ...], ...

PrimeOmega[n] gives the number of prime factors counting multiplicities \[CapitalOmega](n) in n.

PrimitiveRoot[n] gives the smallest primitive root of n.

Mathematica has not only convenient built-in multilingual dictionaries, but also built-in information on word meaning, structure and usage, as well as the relationship ...

The world's largest integrated web of mathematical capabilities and algorithms

In addition to the existing datasets that have been updated, Mathematica 8 now exposes the curated knowledge databases available from Wolfram|Alpha.

"CellGroup" is a front end token that groups selected cells.