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2nd order ODE

  1. Feb 14, 2006 #1
    Hi ,
    I am stuck with the following problem:

    Find a second order linear homogeneous equation having the pair as a fundamental set of solutions:
    y1(x)=x , y2(x)=x*ln(x).

    My problem here is that I dont have the exponential form for the proposed solutions.

    Thank you for your help

  2. jcsd
  3. Feb 15, 2006 #2


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    You don't need an exponential form. Can you find a (single) linear combination of the function and its first and second derivatives that add to zero - for both functions?
  4. Feb 15, 2006 #3
    Ok you mean :
    y1=x ----> (y1)'=1 -------> (y1)"=0
    it gives: x*y' -y=0

    y2(x)=x*ln(x) ----> (y2)'=1+ln(x) -----> (y2)"=1/x
    it gives y*y"-(y'-1)=0

    The second equation seems to be the good one since it is a second degree?
    Am I right?
  5. Feb 15, 2006 #4


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    I don't think there is any need to go nonlinear. Try this:

    x y'' - x y' + y = 0
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