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ode::unimodular

Unimodular transformation of a linear ordinary differential equation

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Syntax

ode::unimodular(Ly, y(x), <Transform>)

Description

ode::unimodular(Ly, y(x)) tests if the linear homogeneous differential equation Ly has a unimodular Galois group (i.e. the wronskian lies in the base field (x)), if not transforms Ly into a unimodular one (by changing the second highest coefficient to zero) and returns a table with index equation and factorOfTransformation containing respectively the transformed differential equation and the factor of transformation Wn such that a solution of the transformed equation multiplied by Wn is a solution of Ly.

If the option Transform is given then Ly is transformed unconditionally even if Ly has yet a unimodular Galois group.

Examples

Example 1

We test if the following differential equation has a unimodular Galois group:

 Ly := y(x)*6+x*diff(y(x),x)*(-2)+diff(y(x),x$2)*(-x^2+1)

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

It is unimodular since the factor of transformation is 1. We can also check this by computing the wronskian of Ly which is a rational function:

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

Now we transform Ly into a differential equation whose wronskian is 1:

ode::unimodular(Ly, y(x), Transform)

ode::wronskian(%[equation], y(x))

Parameters

Ly

A homogeneous linear differential equation over (x).

y(x)

The dependent function of Ly.

Return Values

table.

See Also

MuPAD Functions

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