Mathieu function

As Mathieu differential equation is a special linear ordinary differential equation of second order is called. The DGL is named after the mathematician Émile Léonard Mathieu and is a special case of Hill 's equation with a parameter function

Normal form

The equation is presented in the literature in various forms. An entity known as the normal form equation has the form

X is a function of time

As the abbreviations and for

Alternative representation

The DGL is also indicated, among other things as follows

Solution properties

The Mathieu differential equation can be represented as a linear differential equation of first order system of two equations:

The coefficient matrix is - here periodically. After the set of Floquet can describe the fundamental matrix as

It is also - and periodically. By computing the Jordan normal form of the matrix between two cases: