If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

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 ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

In most cases, you want the head f of a Mathematica expression like f[x] to be a single symbol. There are, however, some important applications of heads that are not symbols. ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

You can ask for information about any object, whether it is built into Mathematica, has been read in from a Mathematica package, or has been introduced by you. Ways to get ...

Here is the integral ∫x^n dx in Mathematica. Here is a slightly more complicated example. Mathematica knows how to do almost any integral that can be done in terms of ...

The replacement operator /. allows you to apply transformation rules to a specific expression. Often, however, you want to have transformation rules automatically applied ...

MathLM Mathematica

Mathematica provides permutation representations for many important finite groups. Some of these groups are members of infinite families, parametrized by one or more ...