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Non-linear 2rd diff. eqtn.

  1. Jun 29, 2011 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=36816&stc=1&d=1309339678.jpg

    2. Relevant equations



    3. The attempt at a solution

    I just want to ask how to obtain the solution?
    What mathematical method involved?
     

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  2. jcsd
  3. Jun 29, 2011 #2

    ehild

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    Replace back the given function into the differential equation and see if it is really the solution.

    ehild
     
  4. Jun 29, 2011 #3
    What makes you think this is Non Linear?
     
  5. Jun 29, 2011 #4

    I just want to know, if I only have the first line, how can I get second line?
    Just by try and error?
     
  6. Jun 29, 2011 #5
    I see there is a square there.:tongue:
     
  7. Jun 29, 2011 #6

    ehild

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    Is the second line solution of the differential equation?

    ehild
     
  8. Jun 29, 2011 #7

    ideasrule

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    It's still linear because neither psi nor the second derivative of psi is being squared. However, the second line isn't the solution, and there's no solution in terms of elementary functions:

    http://www.wolframalpha.com/input/?i=y%27%27%3Dx^2*y
     
  9. Jun 29, 2011 #8
    I saw the eqtn from this book.
    Does it mean that the approximation is wrong?

    attachment.php?attachmentid=36838&stc=1&d=1309409900.jpg
     

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  10. Jun 30, 2011 #9

    ehild

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    If you calculate the second derivative of Ψ=exp(±z2/2) you will find that it is (z2±1)Ψ. Therefore the Ψ-s are only approximate solution, valid for z2>>1.

    ehild
     
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