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ode::polynomialSolutions

Polynomial solutions of a homogeneous linear ordinary differential equation

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

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

Description

ode::polynomialSolutions computes a fundamental set of polynomial solutions of a homogeneous linear ordinary differential equation.

ode::polynomialSolutions returns a fundamental set of the polynomial solutions of Ly, i.e., solutions in the ring . When the option Generic is given, a generic form of them is returned.

Examples

Example 1

We compute the polynomial solutions of the following differential equation:

`Ly:=3*x*diff(y(x),x,x)-x*diff(y(x),x)+9*y(x)`

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

`ode::polynomialSolutions(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