Halm ODEs - Maple Help

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Halm ODEs

 

Description

Examples

Description

• 

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

Halm_ode := (1+x^2)^2*diff(y(x),x,x)+lambda*y(x) = 0;

Halm_ode:=x2+12ⅆ2ⅆx2yx+λyx=0

(1)
  

See Hille, "Lectures on Ordinary Differential Equations", p. 357. The solution to this ODE can be expressed in terms of the hypergeometric function; see hypergeom.

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorHalm_ode

_Halm

(3)

dsolveHalm_ode

yx=_C1x2+1x+Ix+I12λ+1+_C2x2+1x+Ix+I12λ+1

(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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