For which values of m does x^m satisfy the D.E.? Just wanting a double check.

Since I kept getting this wrong last night I thought I should double check with ya'll to make sure I'm doing everything correctly. Thanks.

For which values of m, does satisfy the following D.E.?

So my strategy is to just substitute for y and find the values of m such that the equation equals 0.

After substituting;

there's a cancellation in the first two terms, since

so the discriminant is

and

Re: For which values of m does x^m satisfy the D.E.? Just wanting a double check.

Yes, m= 1/3 and m= -3 are correct.