Results 1 to 1 of 1

Math Help - Annihilator Operators

  1. #1
    Super Member
    Jun 2009
    United States

    Annihilator Operators

    If I have a linear, non-homogeneous differential equation with a function like e^{2x} on the right-side, one of the standard methods is to use an annihilater to transform it to a homogeneous equation.

    The operator (D-\alpha) annihilates functions of this form. However, it's also true that [D^2-2\alpha D+\alpha ^2+\beta ^2]^n annihilates fucntions of the form x^{n-1}e^{\alpha x}cos(\beta x). Using \alpha=2 and \beta =0 and n=1 gives the annihilater (D^2-4D+4)=(D-2)(D-2), so the corresponding auxiliary equation will contain 2 repeated roots for these factors. However, the annihilater (D-2) implies one root.

    I guess in general you can annihilate functions many ways, but using different annihilaters will give different auxiliary equations right?

    EDIT: Wait, \beta >0 is an assumption when deriving the operator, so what I'm doing doesn't make any sense. It also applies to the case that the function is a sine instead of a cosine, which would require a different value of \beta too. However, The differential operator I obtained still seems to work. I tested it.
    Last edited by adkinsjr; February 25th 2011 at 02:09 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: February 26th 2010, 02:29 PM
  2. Annihilator
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 24th 2009, 04:11 PM
  3. Annihilator
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 22nd 2009, 11:43 AM
  4. Annihilator Method?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 12th 2009, 05:04 AM
  5. Annihilator
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 20th 2008, 12:44 PM

Search Tags

/mathhelpforum @mathhelpforum