Laguerre ODEs - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Classifying ODEs : Second Order : odeadvisor/Laguerre

Laguerre ODEs

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, and ?odeadvisor,<TYPE> where <TYPE> is one of: 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; for other differential orders see odeadvisor,types.


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam