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Find the value of n

  1. Sep 18, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Find the value of n so that the equation [itex]V=r^n(3 \cos ^3 \theta -1)[/itex] satisfies the relation
    $$\dfrac{\partial}{\partial r} \left( r^2 \dfrac{\partial V}{\partial r} \right) + \dfrac{1}{\sin \theta}\dfrac{\partial}{\partial \theta} \left( \sin \theta \dfrac{\partial V}{\partial \theta} \right)=0$$


    2. Relevant equations

    3. The attempt at a solution
    The final equation after differentiation comes out to be
    $$n(n+1)(3 \cos ^3 \theta -1) = 18 \cos \theta (2\cos ^2 \theta -1) $$

    What should I substitute for θ ?
     
  2. jcsd
  3. Sep 18, 2014 #2

    Simon Bridge

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    Why should you need to substitute something for theta?
    Recheck your algebra... you final relation is saying there is no value of n that will make V satisfy the PDE.
     
  4. Sep 18, 2014 #3

    utkarshakash

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    I've already checked it thrice but couldn't find any error! Can you please show me where I'm going wrong?
     
  5. Sep 18, 2014 #4

    Ray Vickson

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    How can anybody tell where you went wrong? You have not shown your work in detail.

    I (or Maple) get something completely different from your result.
     
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