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# ode::isFuchsian

Tests if a homogeneous linear ordinary differential equation is of Fuchsian type

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```ode::isFuchsian(Ly, y(x), <AllExponents>)
```

## Description

ode::isFuchsian returns TRUE if Ly is of Fuchsian type, i.e., all the singular points (including the point at infinity) of Ly are regular. It returns FALSE if at least one singular point is irregular. When the option AllExponents is given, either FALSE is returned or a list where each element is a table containing, at each regular singular point of Ly the place, the indicial equation and the exponents.

## Examples

### Example 1

We test if the following differential equation is Fuchsian:

`Ly:=x*(1-x)*diff(y(x),x\$2)+(1-x)*diff(y(x),x)+10*y(x)`

`ode::isFuchsian(Ly, y(x))`

We can have a look of the indicial equations, exponents at each regular singular point of Ly:

`ode::isFuchsian(Ly, y(x), AllExponents)`

### Example 2

In this example, the Airy equation, the only singular point is at infinity and is irregular:

`ode::isFuchsian(diff(y(x),x\$2)-x*y(x), y(x))`

## Parameters

 Ly A homogeneous linear ordinary differential equation with coefficients in the field ℚ(x) of rational functions over the rationals. y(x) The dependent function of Ly.

## Options

 AllExponents Return a list of tables of indical equations and exponents for regular singular points.

## Return Values

TRUE, FALSE or a list.