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# ode::rationalSolutions

Rational solutions of a homogeneous linear ordinary differential equation

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```ode::rationalSolutions(Ly, y(x), <Generic>)
```

## Description

ode::rationalSolutions returns a fundamental set of the rational solutions of Ly, i.e., solutions in the field (x). When the option Generic is given, a generic form of them is returned.

## Examples

### Example 1

We compute the rational solutions of the following differential equation:

```Ly:=(4*x^5+8*x^3+4*x)*diff(y(x),x,x)+
(36*x^4+32*x^2-4)*diff(y(x),x)+48*x^3*y(x)```

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

`ode::rationalSolutions(Ly, y(x), Generic)`

## 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.

## Return Values

set, possibly empty, of functions or an expression