NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

Mathematica provides powerful functions for constructing lists of any size and structure.

DivisorSigma[k, n] gives the divisor function \[Sigma]_k (n).

Trig is an option for various polynomial manipulation functions that specifies whether trigonometric functions should be treated like polynomial elements.

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

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

Expand[expr] expands out products and positive integer powers in expr. Expand[expr, patt] leaves unexpanded any parts of expr that are free of the pattern patt. >

CoprimeQ[n_1, n_2] yields True if n_1 and n_2 are relatively prime, and yields False otherwise. CoprimeQ[n_1, n_2, ...] yields True if all pairs of the n_i are relatively ...

SeriesCoefficient[series, n] finds the coefficient of the n\[Null]\[Null]^th-order term in a power series in the form generated by Series. SeriesCoefficient[f, {x, x_0, n}] ...