Basis of solutions

1. Oct 16, 2005

asdf1

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. Oct 16, 2005

Tide

Have you learned power series methods (Frobenius) for solving linear ODEs?

3. Oct 17, 2005

asdf1

no, not yet

4. Oct 17, 2005

HallsofIvy

Staff Emeritus
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!)

5. Oct 18, 2005

asdf1

ok, i'll try that!