Laguerre ODEs - Maple Programming Help

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Laguerre ODEs

 

Description

Examples

Description

• 

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

Laguerre_ode := x*diff(y(x),x,x)+(a+1-x)*diff(y(x),x)+lambda*y(x) = 0;

Laguerre_ode:=xⅆ2ⅆx2yx+a+1xⅆⅆxyx+λyx=0

(1)
  

See Iyanaga and Kawada, "Encyclopedic Dictionary of Mathematics", p. 1481. The solution to this type of ODE can be expressed in terms of the WhittakerW and WhittakerM functions.

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorLaguerre_ode

_Laguerre

(3)

dsolveLaguerre_ode

yx=_C1KummerMλ,a+1,x+_C2KummerUλ,a+1,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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