My original question was
Solve $$x^2y'' + 2y' - 2y = 0$$
First I noticed that $x^2+2x+2$ is a solution. Using order reduction, doing $y = v(x)(x^2+2x+2)$, I found that $$\int\frac{e^{2/x}}{(x^2+2x+2)^2}dx$$
Can someone help me in this part, please? The only method I found used complex numbers and the $Ei$ function, but I would like a solution in another way.
Thanks for attention.