Laguerre ODEs
Description
Examples
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+1−xⅆⅆxyx+λyx=0
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.
withDEtools,odeadvisor
odeadvisor
odeadvisorLaguerre_ode
_Laguerre
dsolveLaguerre_ode
yx=c__1KummerM−λ,a+1,x+c__2KummerU−λ,a+1,x
See Also
DEtools
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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