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Is this diff eq solvable?

  1. Feb 29, 2008 #1
    Is this diff eq solvable? !!!

    1. The problem statement, all variables and given/known data
    Find the general solution to the third order homogeneous diff eq if one solution is known to be:

    [tex]x^2e^{5x}[/tex]


    I was thinking of using reduction of order but I don't have the original equation!
     
  2. jcsd
  3. Feb 29, 2008 #2
    Okay. Since it was given that the 3rd order diff eq is homogeneous, it is okay to assume that there is no particular solution to this, right?

    And I can also assume that (m-5) is a factor of the characteristic equation. I am also assuming that it is a thrice repeated root, so [itex]y=c_1e^{5x}+c_2xe^{5x}+c_3x^2e^{5x} [/itex]

    I am not so confident in this, since it is all based on assumption. Any thoughts on the validity of this?
     
  4. Feb 29, 2008 #3
    It might help a bit if you told us what the differential equation was.
     
  5. Feb 29, 2008 #4
    Read the OP. It has not been given.
     
  6. Feb 29, 2008 #5

    HallsofIvy

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    Assuming this is a linear homogeneous 3rd order diff eq with constant coefficients, then that is the case and the differential equation must be (D- 5)3y= y"'-15y"+ 75y'- 125y= 0. Of course, we were not told that.
     
    Last edited: Feb 29, 2008
  7. Feb 29, 2008 #6
    So, as it stands, this problem has been worded incorrectly. That is what I thought. Thank you.
     
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