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Thread: Find the differential operator that annihilates

  1. #1
    Member diddledabble's Avatar
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    Post Find the differential operator that annihilates

    $\displaystyle x^{2}e^{x}-xsin4x+x^{3}$
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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
    $\displaystyle x^{2}e^{x}-xsin4x+x^{3}$
    See this and see if you can figure it out from there.

    Another thing to note is the following: If $\displaystyle L_1,L_2,L_3$ are annihilators of $\displaystyle f(x),g(x),h(x)$ respectively, then $\displaystyle L_1L_2L_3$ annihilates $\displaystyle f(x)+g(x)+h(x)$.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by diddledabble View Post
    $\displaystyle x^{2}e^{x}-xsin4x+x^{3}$
    If you want to check.
    Spoiler:

    $\displaystyle (D-1)^3$ will annihilate the first, $\displaystyle \left(D^2+16\right)^2$ will annihilate the second while $\displaystyle D^4$ will do the third. Then compose the three operators.
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