1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ODE with non-constant coefficient

  1. Jul 4, 2011 #1
    [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: Jul 4, 2011
  2. jcsd
  3. Jul 7, 2011 #2

    lanedance

    User Avatar
    Homework Helper

    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: Jul 7, 2011
  4. Jul 7, 2011 #3

    lanedance

    User Avatar
    Homework Helper

    froma mathematica check it looks like the solutions involve hermite polynomials and other complex functions
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook