Regular Singular Points

For those that are interested, the problem has been taken from the Elementary Differential Equations and Boundary Value Problems, 8th Edition, by Boyce. It is problem 1 from Section 5.4.

The problem states to find all singular points of the given equation and determine whether each one is regular or irregular.

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

$ P(x) = x = 0 $

The point x = 0 is a singular point.

So all other points are ordinary points.

$ \lim_{x \to 0} (x - 0) \frac {(1 - x)} {(x)} = 1 $

$ \lim_{x \to 0} (x - 0)^2 \frac {(x)} {(x)} = 0 $

So as my conclusion the two limits are finite numbers and we can say that the point x = 0 is a regular singular point