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I have the following question regarding a differential equation:

Consider the differential equation $(1-x)y''+y=0$. The problem then asks to find a nonzero power series solution centered about $x=1$. However, this appears to not be possible since $\frac{1}{1-x}$ is not analytic at $x=1$. So how can I find a nonzero series solution to this equation?

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