Gegenbauer ODEs - Maple Programming Help

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Gegenbauer ODEs

 

Description

Examples

Description

• 

The general form of the Gegenbauer ODE is given by the following:

Gegenbauer_ode := (x^2-1)*diff(y(x),x,x)-(2*m+3)*x*diff(y(x),x)+lambda*y(x)=0;

Gegenbauer_ode:=x21ⅆ2ⅆx2yx2m+3xⅆⅆxyx+λyx=0

(1)
  

where m is an integer. See Infeld and Hull, "The Factorization Method". The solution of this type of ODE can be expressed in terms of the LegendreQ and LegendreP functions:

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorGegenbauer_ode

_Gegenbauer

(3)

dsolveGegenbauer_ode

yx=_C1x2154+12mLegendrePm2λ+4m+412,52+m,x+_C2x2154+12mLegendreQm2λ+4m+412,52+m,x

(4)

See Also

DEtools

odeadvisor

dsolve

quadrature

missing

reducible

linear_ODEs

exact_linear

exact_nonlinear

sym_Fx

linear_sym

Bessel

Painleve

Halm

Gegenbauer

Duffing

ellipsoidal

elliptic

erf

Emden

Jacobi

Hermite

Lagerstrom

Laguerre

Liouville

Lienard

Van_der_Pol

Titchmarsh

odeadvisor,types

 


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