Find the general solution of the second ordinary linear homogeneous differential equation when a singular solution is a second order polynomial.

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I am having problem solving an ODE.

This is the equation:

$(x-1)y'' - (x+1)y' + 2y = 0$

So I started with y1 = ax^2 + bx + c, and since this is a solution I substituted its first and second order derivative on the equation and I got stuck here: bx + 2c - 2a = 0

Can anyone help?

(I tried another example that had an exponential solution and it worked cuz I could factor stuff and all but here it's just ?! Maybe I did sth wrong?)