# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# `ode`::`symmetricPower`

Symmetric power of a homogeneous linear ordinary differential equation

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```ode::symmetricPower(`Ly`, y(`x`), `m`)
```

## Description

`ode::symmetricPower(Ly, y(x), m)` computes the m-th symmetric power of `Ly`. This is the lowest order linear ordinary differential equation whose solution space consists exactly of all possible m-th powerproducts of solutions of `Ly`.

## Examples

### Example 1

We compute the second symmetric power of the following differential equation:

`Ly:=x^2*diff(y(x),x\$2)-(36*x^6*exp(4*x^3)+9*x^6+2)*y(x)`

`ode::symmetricPower(Ly, y(x), 2)`

## Parameters

 `Ly` A homogeneous linear ordinary differential equation. `y(x)` The dependent function of `Ly`. `m` A positive integer.

## Return Values

Linear differential equation