1. Not finding help here? Sign up for a free 30min 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!

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
    Staff Emeritus
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?