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Homework Help: Second order homog. DE non-const coeff.

  1. Jul 21, 2005 #1
    I have a 2nd order homogeneous non-const. coefficients linear DE, and don't remember how we used to solve it or even if we did at all, looked through the book, but it only covers a case of Cauchy-Euler.

    The original question actually goes like this:
    verify that y(x) = sin (x2) is in the kernel of L,
    L = D2 - x-1D + 4x2, where D is a differetiation operator.

    so what I have so far is this:
    Ly = 0
    when I distribute I get this DE and get stuck with it:

    y'' - x-1y' + 4x2y = 0

    Thanks for any help.
  2. jcsd
  3. Jul 21, 2005 #2


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    This is a very simple question, just insert sin(x^2) for y.

  4. Jul 21, 2005 #3
    shoot...i need sleep. :yuck:

    Thanks :smile:
  5. Jul 21, 2005 #4


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    Homework Helper

    Good night, sleep tight! :zzz:

  6. Jul 21, 2005 #5


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    Science Advisor
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    sleep...highly recommended
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