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Differential operator

  1. Nov 11, 2005 #1
    for the following question:
    [4(x^2)(D^2)+12xD+3)]y=0

    my problem:
    i only know how to solve this type of question if i change it back to its original form. however, if i want to solve it by just using D, how would i do that?
     
  2. jcsd
  3. Nov 12, 2005 #2

    quasar987

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    What do you mean its original form?

    And what are you expected to do with this equation anyway?
     
  4. Nov 12, 2005 #3
    i mean that if i changed the D to y``
     
  5. Nov 12, 2005 #4

    quasar987

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    OH! Well I guess just treat Dy as dy/dx and solve as you would.
     
  6. Nov 12, 2005 #5

    saltydog

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    I looked at it early this morning and even briefly posted what I though was the factored form of the differential operators and even though it resulted in a correct answer, my factored version was incorrect because the differential operators are NOT commutative. Turns out equations with functions of x are not easily factored for this reason, something I'm not clear on. So I would just treat it as a regular Euler-Cauchy equation and look for a solution of the form:

    [tex]y=x^{m}[/tex]

    (unless someone can further comment about the factoring).:smile:
     
    Last edited: Nov 12, 2005
  7. Nov 13, 2005 #6
    i had the same problem as you when i tried to factor it too~
     
  8. Nov 14, 2005 #7
    This ia a quadratic in D.Just find out D using the formula used for quadratic equations and then proceed
     
  9. Nov 14, 2005 #8

    HallsofIvy

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    The whole point is that this is an equation with VARIABLE coefficients. That method doesn't work with variable coefficients.
     
  10. Nov 14, 2005 #9
    @@ why doesn't it work for variable coefficients?
     
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