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Factorising and integrating a differential

  1. Apr 28, 2012 #1
    Having a bit of trouble with this equation, I need to find V explicitly and this would obviously be done by factorising and integrating, but I can't seem to factorise it correctly. I have what I think is the correct answer but can't do the steps to get there. Any help would be greatly appreciated.

    δ2V/δr2 + 1/r δV/δr - V/r = 0

    which I think goes to:

    V = C1r/2 + C2/r

    C1 and C2 being constants of integration.
  2. jcsd
  3. Apr 28, 2012 #2


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    hi eddysd! :smile:
    no, i think that would be δ2V/δr2 + 1/r δV/δr - V/r2 = 0
  4. Apr 28, 2012 #3
    Yes sorry, typo, that is the correct equation! Do you think you could tell me how to get from that to the equation for V?
  5. Apr 28, 2012 #4
    Solutions involves Bessel functions.
  6. Apr 28, 2012 #5
    substiution r=exp(y) will give you the required answer .To know why multiply the eqn by r^2 and see the second term and it does not involve bessel functions.
    Last edited: Apr 28, 2012
  7. Apr 28, 2012 #6
    Now it is an homogeneous ODE.
    So, use the classical method : Let V=r*W and rewite the ODE where W is the unknown function.
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