The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

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 ...

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 ...

"Defining Variables" discussed assignments such as x=y which set x equal to y. Here we discuss equations, which test equality. The equation x==y tests whether x is equal to ...

Mathematica allows you to export graphics and sounds in a wide variety of formats. If you use the notebook front end for Mathematica, then you can typically just copy and ...

Dealing with fonts under Linux can sometimes be tricky. The important issues in dealing with fonts in Mathematica are presented in this tutorial for your convenience. The ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

Important points to remember in Mathematica. If you have used other computer systems before, you will probably notice some similarities and some differences. Often you will ...

In many cases, you will find it convenient to communicate with external programs at a high level, and to exchange structured data with them. On almost all computer systems, ...

Low-level functions for converting between expressions and boxes. MakeBoxes generates boxes without evaluating its input. MakeExpression interprets boxes but uses ...