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ode::isLODE

Test for a linear ordinary differential equation

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Syntax

ode::isLODE(Ly, y(x), <Homogeneous | HlodeOverRF | Hlode | LodeOverRF | Lode>)

Description

ode::isLODE(Ly, y(x)) returns TRUE if Ly is a linear ordinary differential equation in y(x), FALSE otherwise. If an optional argument is given then the result is discussed as follows:

  • Homogeneous: returns TRUE if Ly is homogeneous, FALSE otherwise.

  • HlodeOverRF: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is homogeneous with rational functions coefficients, FALSE otherwise.

  • Hlode: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is homogeneous, FALSE otherwise.

  • LodeOverRF: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly has rational functions coefficients, FALSE otherwise.

  • Lode: returns the sequence Ly, y, x, n, where n is the order of Ly, if Ly is a linear ordinary differential equation, FALSE otherwise.

Examples

Example 1

We test the following differential equations:

ode::isLODE(y(x)^2+x^2*diff(y(x),x)+x, y(x))

ode::isLODE(y(x)+x^2*diff(y(x),x)+x, y(x))

ode::isLODE(y(x)+x^2*diff(y(x),x)+x, y(x), Hlode)

ode::isLODE( 
     y(x)+x^2*diff(y(x),x)+x*diff(y(x),x$2), y(x), HlodeOverRF)

ode::isLODE( 
     x+x^2*diff(y(x),x)+exp(x)*diff(y(x),x$2), y(x), LodeOverRF)

Parameters

Ly

An expression.

y(x)

The dependent function of Ly.

Return Values

Either TRUE, FALSE or a sequence of type _exprseq.

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