# Documentation

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# `ode`::`vectorize`

Coefficients of a homogeneous linear ODE

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## Syntax

```ode::vectorize(`Ly`, `y`, `x`, `n`)
```

## Description

`ode::vectorize(Ly, y, x, n)` returns the list of coefficients of the `n`-th order homogeneous linear ordinary differential equation `Ly`.

## Examples

### Example 1

We compute the list of coefficients of the following differential equation:

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

`ode::vectorize(Ly, y, x, 3)`

## Parameters

 `Ly` A homogeneous linear ordinary differential equation. `y` The dependent variable of `Ly`. `x` The independent variable of `Ly`. `n` The order of `Ly`, a positive integer.

`list`