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Math Help - Separation of variables in polar coordinates - Question

  1. #1
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    Separation of variables in polar coordinates - Question

    Hey guys, Im stuck on the question below. I know how to go about things if the RHS is 0, but with the sine on the RHS Im not sure what to do.




    Cheers guys.
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  2. #2
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    Using there hint seek a solution in the form

     <br />
u(r,\theta) = \sum_{n=1}^{\infty} R_n(r)\sin 2 n \theta<br />
.

    When you sub in your PDE you obtain

     <br />
\sum_{n=1}^{\infty} \left( R_n'' + \frac{R_n'}{r} - \frac{4n^2 R_n}{r^2}\right) \sin 2 n \theta = r \sin 2 \theta.<br />

    Now start indexing n and compare LHS to RHS. You'll get a set of ODEs for R_n.
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  3. #3
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    Thanks a lot!!

    Much appreciated.
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