Bessel and Modified Bessel ODEs - Maple Programming Help

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Bessel and Modified Bessel ODEs

 

Description

Examples

Description

• 

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

Bessel_ode := x^2*diff(y(x),x,x)+x*diff(y(x),x)+(x^2-n^2)*y(x);

Bessel_ode:=x2ⅆ2ⅆx2yx+xⅆⅆxyx+n2+x2yx

(1)
• 

The general form of the modified Bessel ODE is given by the following:

modified_Bessel_ode := x^2*diff(y(x),x,x)+x*diff(y(x),x)-(x^2+n^2)*y(x);

modified_Bessel_ode:=x2ⅆ2ⅆx2yx+xⅆⅆxyxn2+x2yx

(2)
  

where n is an integer. See Abramowitz and Stegun - `Handbook of Mathematical Functions`, section 9.6.1. The solutions for these ODEs are expressed using the Bessel functions in the following examples.

Examples

withDEtools,odeadvisor

odeadvisor

(3)

odeadvisorBessel_ode

_Bessel

(4)

odeadvisormodified_Bessel_ode

_Bessel,_modified

(5)

The Bessel ODEs can be solved for in terms of Bessel functions:

dsolveBessel_ode

yx=_C1BesselJn,x+_C2BesselYn,x

(6)

dsolvemodified_Bessel_ode

yx=_C1BesselIn,x+_C2BesselKn,x

(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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