How to go about finding the second independent linear series solution through reduction of order (infinite series diff. eq)?

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$x^2y[''] + 2y['] +2[y] = 0$

irregular singular point $x=0$

How would I go about the reduction process to find $y2(x)$ (the second linearly independent solution)? This is a textbook solution and no one online has attempted to find the second linear independent solution or even explain how to to go about the process either.

For reference, I already got $y1(x)$ which

$y1(x)=1+x+(1/2)x^2 + ...$

and the problem only requires finding the first three nonzero terms of the series expansion

Thank you