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Differential eqtn (What's wrong with my calculation?)

  1. Jul 2, 2011 #1
    I would like to ask why I obtain a different answer from the book?
    If I am wrong, how to obtain the correct answer?

    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=36887&stc=1&d=1309589655.jpg

    2. Relevant equations



    3. The attempt at a solution

    attachment.php?attachmentid=36888&stc=1&d=1309589655.jpg
     

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  2. jcsd
  3. Jul 2, 2011 #2

    vela

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    Rewrite the differential equation slightly to get
    [tex]\rho^2u''(\rho)-l(l+1)u(\rho) = 0[/tex]
    Then substitute a trial solution of the form [itex]\rho^r[/itex] and then solve for r.
     
  4. Jul 2, 2011 #3
    Is it another way to solve ODE?
    What is the name of this method?

    I can only remember to sub e^r:tongue2:
     
  5. Jul 2, 2011 #4

    vela

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  6. Jul 2, 2011 #5

    HallsofIvy

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    You basic error is trying to apply a method that works for equations with constant coeficients to an equation with variable coefficients. As a result your characteristic equation, which should not involve the idependent variable, is wrong and everything after that is wrong.
     
  7. Jul 2, 2011 #6
    attachment.php?attachmentid=36892&stc=1&d=1309611050.jpg

    how about this one?
    How to solve it?
     

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  8. Jul 2, 2011 #7

    Gib Z

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