I'm having trouble getting this question started. Im not sure how to go about solving it nor what method to use. Some of my friends say to divide by $\displaystyle x^2$, while others tell me other ways.

$\displaystyle x^2 d^2 y/ dx^2 + 2x (x-1) dy/dx - 2(x-1)y=0$

Why doesn't the general theory guarantee a unique solution to the equation satisfying the initial conditions y(0) = 0, y'(0) = 1.

If someone could explain to me what i need to do, i would much appreciate it

thanks