A Bernoulli equation is a first-order equation of the form The problem of solving equations of this type was posed by James Bernoulli in 1695. A year later, in 1696, G. ...

An Euler equation is an ODE of the form The following is an example of an Euler equation. The Legendre linear equation is a generalization of the Euler equation. It has the ...

A linear ordinary differential equation of order n is said to be exact if The condition of exactness can be used to reduce the problem to that of solving an equation of order ...

The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is a ...

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

In an expression like f[x], the 'function name' f is itself an expression, and you can treat it as you would any other expression. You can replace names of functions using ...

"Redrawing and Combining Plots" describes how you can make regular arrays of plots using GraphicsGrid. Using the Inset graphics primitive, however, you can combine and ...

This does an integral over the interior of the unit circle. Here is an equivalent form. Even though an integral may be straightforward over a simple rectangular region, it ...

Basic Objects Input Syntax Some General Notations and Conventions

If you enter text in languages other than English, you will typically need to use various additional accented and other characters. If your computer system is set up in an ...