Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    Tide

    User Avatar
    Science Advisor
    Homework Helper

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

    HallsofIvy

    User Avatar
    Science Advisor

    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!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook