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# ode::ratSys

Rational solutions of a first order homogeneous linear differential system

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```ode::ratSys(M, x)
```

## Description

ode::ratSys(M, x) computes a fundamental set of rational solutions of the first order homogeneous linear differential system Y'=MY. This method uses a cyclic vector and therefore is not optimal.

## Examples

### Example 1

We compute the rational solutions of the following differential system:

```A := matrix([ [2*(x+x^2-9)/x/(x-2),2*(x^2-6)/x/(x-2)],
[-3*(2*x+x^2-12)/x/(x-2),-(2*x+3*x^2-24)/x/(x-2)] ])```

`v := ode::ratSys(A, x)`

And we can check the result:

`diff(v[1], x) = normal(A*v[1])`

## Parameters

 M A square matrix of type Dom::Matrix with coefficients in the field ℚ(x) of rational functions over the rationals. x The independent function.

## Return Values

set, possibly empty, of objects of type Dom::Matrix.