The Error Function (erf) ODE - Maple Programming Help

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The Error Function (erf) ODE

 

Description

Examples

Description

• 

The general form of the erf ODE is given by

erf_ode := diff(y(x),x,x)+2*x*diff(y(x),x)-2*n*y(x) = 0;

erf_ode:=ⅆ2ⅆx2yx+2xⅆⅆxyx2nyx=0

(1)
  

where n is an integer. See Abramowitz and Stegun, "Handbook of Mathematical Functions", section 7.2.2. The solution of this type of ODE can be expressed in terms of the WhittakerM and WhittakerW functions.

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorerf_ode

_erf

(3)

dsolveerf_ode

yx=_C1ⅇx2KummerM1+12n,32,x2x+_C2ⅇx2KummerU1+12n,32,x2x

(4)

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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