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ode::companionSystem

Companion matrix of a linear homogeneous ordinary differential equation

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Syntax

ode::companionSystem(Ly, y(x), <R>)

Description

ode::companionSystem(Ly, y(x)) returns the companion matrix associated to Ly. If the optional argument R is given, the elements of the matrix are in R.

Examples

Example 1

We compute the companion matrix of the following differential equation:

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

ode::companionSystem(Ly, y(x))

Parameters

Ly

A linear homogeneous ordinary differential equation.

y(x)

The dependent function of Ly.

R

A field of functions or numbers of characteristic zero, default is Dom::ExpressionField(normal).

Return Values

Object of type Dom::Matrix.

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