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Can someone help me i don't understand this DE

  1. Jul 4, 2013 #1
    problem: xy''-4y'=x^4

    when i solve it i get y(homogeneous)=C1+C2x^5 which is fine because that's what the back of the book says

    but for the particular solution, i get .. C1=-(1/25)x^5 , C2=(1/5)lnx

    so y(general)= C1+C2x^5-(1/25)x^5+(1/5)lnx(x^5)

    but wolframalpha as well as the back of my book both say the answer is...

    where does the -(1/25)x^5 term go?....
  2. jcsd
  3. Jul 4, 2013 #2


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    You have
    C1 x5 + C2 x5 = C3x5

    Does that help?
    Last edited: Jul 4, 2013
  4. Jul 4, 2013 #3
    so technically my answer is correct and they just combined the x^5 terms.. i see
  5. Jul 4, 2013 #4
  6. Jul 10, 2013 #5


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    Gold Member

    If you're finding the general solution of an ODE, then usually you would not allow pieces of the homogeneous solution to show up in the particular solution.
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