# 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!