Halm ODEs - Maple Help

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Halm ODEs

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, 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.


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