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 ...

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

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 ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...

A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...

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 ...

A standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With Mathematica, however, you can often get exact results. ...

Mathematica notebooks provide the basic technology that you need to be able to create a very wide range of sophisticated interactive documents. But to get the best out of ...

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 ...