Halm ODEs
Description
Examples
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
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.
withDEtools,odeadvisor
odeadvisor
odeadvisorHalm_ode
_Halm
dsolveHalm_ode
yx=c__1x2+1x+I−x+Iλ+12+c__2x2+1x+I−x+I−λ+12
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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