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Math Help - Find the differential operator that annihilates

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

    x^{2}e^{x}-xsin4x+x^{3}
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by diddledabble View Post
    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 L_1,L_2,L_3 are annihilators of f(x),g(x),h(x) respectively, then L_1L_2L_3 annihilates 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
    x^{2}e^{x}-xsin4x+x^{3}
    If you want to check.
    Spoiler:

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