Linear Second Order ODE/x^2 y'' - 2 x y' + 2 y = 0

Theorem
The second order ODE:
 * $(1): \quad x^2 y'' - 2 x y' + 2 y = 0$

has the general solution:
 * $y = C_1 x + C_2 x^2$

on any closed real interval which does not contain $0$.