Complete Elliptic Integral ODEs - Maple Programming Help

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Complete Elliptic Integral ODEs

 

Description

Examples

Description

• 

The general forms of the elliptic ODEs are given by the following:

elliptic_I_ode := diff(x*(1-x^2)*diff(y(x),x),x)-x*y(x)=0;

elliptic_I_ode:=x2+1ⅆⅆxyx2x2ⅆⅆxyx+xx2+1ⅆ2ⅆx2yxxyx=0

(1)

elliptic_II_ode := (1-x^2)*diff(x*diff(y(x),x),x)+x*y(x)=0;

elliptic_II_ode:=x2+1ⅆⅆxyx+xⅆ2ⅆx2yx+xyx=0

(2)
  

See Gradshteyn and Ryzhik, "Tables of Integrals, Series and Products", p. 907. The solution to this type of ODE can be expressed in terms of the EllipticK and EllipticCK functions.

Examples

withDEtools,odeadvisor

odeadvisor

(3)

dsolveelliptic_I_ode

yx=_C1EllipticKx+_C2EllipticCKx

(4)

dsolveelliptic_II_ode

yx=_C1EllipticEx+_C2EllipticCExEllipticCKx

(5)

odeadvisorelliptic_I_ode

_elliptic,_class_I

(6)

odeadvisorelliptic_II_ode

_elliptic,_class_II

(7)

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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