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# ode::isLODE

Test for a linear ordinary differential equation

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```ode::isLODE(Ly, y(x), <Homogeneous | HlodeOverRF | Hlode | LodeOverRF | Lode>)
```

## Description

ode::isLODE(Ly, y(x)) returns TRUE if Ly is a linear ordinary differential equation in y(x), FALSE otherwise. If an optional argument is given then the result is discussed as follows:

• Homogeneous: returns TRUE if Ly is homogeneous, FALSE otherwise.

• HlodeOverRF: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is homogeneous with rational functions coefficients, FALSE otherwise.

• Hlode: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is homogeneous, FALSE otherwise.

• LodeOverRF: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly has rational functions coefficients, FALSE otherwise.

• Lode: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is a linear ordinary differential equation, FALSE otherwise.

## Examples

### Example 1

We test the following differential equations:

`ode::isLODE(y(x)^2+x^2*diff(y(x),x)+x, y(x))`

`ode::isLODE(y(x)+x^2*diff(y(x),x)+x, y(x))`

`ode::isLODE(y(x)+x^2*diff(y(x),x)+x, y(x), Hlode)`

```ode::isLODE(
y(x)+x^2*diff(y(x),x)+x*diff(y(x),x\$2), y(x), HlodeOverRF)```

```ode::isLODE(
x+x^2*diff(y(x),x)+exp(x)*diff(y(x),x\$2), y(x), LodeOverRF)```

## Parameters

 Ly An expression. y(x) The dependent function of Ly.

## Return Values

Either TRUE, FALSE or a sequence of type _exprseq.