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Hermite ODEs

 

Description

Examples

References

Description

• 

The general form of the Hermite ODE is given by the following.

Hermite_ode := diff(y(x),x,x) = 2*x*diff(y(x),x)-2*n*y(x);

Hermite_odeⅆ2ⅆx2yx=2xⅆⅆxyx2nyx

(1)
  

where n is an integer. The solution of this type of ODE can be expressed in terms of hypergeometric or Whittaker functions.

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorHermite_ode

_2nd_order,_with_linear_symmetries

(3)

dsolveHermite_ode

yx=c__1xKummerM12n2,32,x2+c__2xKummerU12n2,32,x2

(4)

dsolveHermite_ode,hypergeometric

yx=c__1KummerMn2,12,x2+c__2KummerUn2,12,x2

(5)

References

  

Abramowitz, M., and Stegun, I. Handbook of Mathematical Functions, section 22.6.21. Dover Publications.

See Also

DEtools

dsolve

hypergeometric

odeadvisor

odeadvisor/TYPES

Whittaker