Jacobi ODEs - Maple Help

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Jacobi ODEs

Description

• 

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

Jacobi_ode := diff(y(x),x,x)*x*(1-x) = (g-(a+1)*x)*diff(y(x),x)+n*(a+n)*y(x);

Jacobi_ode:=ⅆ2ⅆx2yxx1x=ga+1xⅆⅆxyx+na+nyx

(1)
  

where n is an integer. See Iyanaga and Kawada, "Encyclopedic Dictionary of Mathematics", p. 1480.

Examples

The solution to this type of ODE can be expressed in terms of the hypergeometric function; see hypergeom.

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorJacobi_ode

_Jacobi

(3)

dsolveJacobi_ode

yx=_C1hypergeom112a12a2+4n+4a4n2+4,112a+12a2+4n+4a4n2+4,g,x+_C2x1+ghypergeom12a12a2+4n+4a4n2+4+g,12a+12a2+4n+4a4n2+4+g,2+g,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.


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