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Basis of solutions

  1. Oct 16, 2005 #1
    for the following question:
    find a basis of solutions for
    (x^2)y`` -xy`+y=0

    my problem:
    i haven't a clue on where to start~
    can someone give some tips for starters?
  2. jcsd
  3. Oct 16, 2005 #2


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    Have you learned power series methods (Frobenius) for solving linear ODEs?
  4. Oct 17, 2005 #3
    no, not yet
  5. Oct 17, 2005 #4


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    It's not necessary to use power expansions here. This is an "Euler-type" or "equipotential" equation- the degree of x in each term is equal to the order of the derivative.

    Hint- let y= xr for unknown r, then find r so that the equation is satisfied.

    (That will get you started, but that's actually the easy part!)
  6. Oct 18, 2005 #5
    ok, i'll try that!
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