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Math Help - Annilator Method Error

  1. #1
    Member diddledabble's Avatar
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    Question Annilator Method Error

    Find the annihilator given y''-6y'+10y = e^(3x)-x
    My book list the annihilator as D^3(D-3) but I don't understand how they got that. I am wondering if it might be a typo in the text.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by diddledabble View Post
    Find the annihilator given y''-6y'+10y = e^(3x)-x
    My book list the annihilator as D^3(D-3) but I don't understand how they got that. I am wondering if it might be a typo in the text.
    The Annihilator for e^{3x} is \left(D-3\right) and the annihilator for -x is D^{\color{red}2}.

    Now, the annihilator of e^{3x}-x is the product of the two individual annihilators: D^2\left(D-3\right)

    Note that D^3\left(D-3\right) also works as an annihilator, but D^3 really isn't necessary.

    Now if the question was find the annihilator for e^{3x}-x^2, then the answer your book gives would be correct.

    Does this make sense?
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