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ode::symmetricPower

Symmetric power of a homogeneous linear ordinary differential equation

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Syntax

ode::symmetricPower(Ly, y(x), m)

Description

ode::symmetricPower(Ly, y(x), m) computes the m-th symmetric power of Ly. This is the lowest order linear ordinary differential equation whose solution space consists exactly of all possible m-th powerproducts of solutions of Ly.

Examples

Example 1

We compute the second symmetric power of the following differential equation:

Ly:=x^2*diff(y(x),x$2)-(36*x^6*exp(4*x^3)+9*x^6+2)*y(x)

ode::symmetricPower(Ly, y(x), 2)

Parameters

Ly

A homogeneous linear ordinary differential equation.

y(x)

The dependent function of Ly.

m

A positive integer.

Return Values

Linear differential equation

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