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, ...

 

NumberFieldRegulator[a] gives the regulator of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

ToRadicals[expr] attempts to express all Root objects in expr in terms of radicals.

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

NumberFieldFundamentalUnits[a] gives a list of fundamental units for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Mathematica is widely used throughout the world for precollege education, in mathematics and many other fields. This page lists a few Mathematica functions used particularly ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

 

Mathematica has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of ...