Question

Consider the differential equation

xy"" + 2y' + xy = 0

I have found the two indicial root that is , r = 0 and r = -1

The question requires me to use the smaller root , find the two linearly independent solutions of the diffrential equation.

My question would be ,

1) if i use the smaller one as the finder , do i still apply the same formula to find the second root?

2) Does the question require me to proof that they are linearly independent?

Thank you in advance.=)