The Error Function (erf) ODE - Maple Help

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The Error Function (erf) ODE

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, 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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