Finding a power series solution for a differential equation about a singular point

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?