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ODE with non-constant coefficient

  • Thread starter PhDorBust
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  • #1
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[tex]R'' + 2rR' - Rl(l+1) = 0[/tex], where [tex]R = R(r)[/tex] and l is a constant. This is portion of sol'n by seperation by variables to laplace's equation in spherical coordinates.

I tried laplace transform, but reached integral that I don't think admits analytic sol'n.

[tex]F'(s) + F(s)[\frac{1 + l(l+1)}{s} - s] = sA + B[/tex], where R(0) = A, R'(0) = B.

What am i missing? Is series sol'n the only way?
 
Last edited:

Answers and Replies

  • #2
lanedance
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series sounds like a good idea for this type of problem asnd would be my first approach - is there reason you don't want to use it, or is an analytic expression just going to be simpler to deal with?
 
Last edited:
  • #3
lanedance
Homework Helper
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froma mathematica check it looks like the solutions involve hermite polynomials and other complex functions
 

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