Solve the initial value problem x²y′′−2xy'2+2y=0 with y(1)=0 and y′(1)=2. The general solution for this differential equation is:
a) y=c₁x+c₂x²
b) y=c₁x²+c₂x
c) y=c₁x²+c₂x³
d) y=c₁x+c₂x³