Singular Point

Given the definition of an ordinary point:

Given a Second Order homogenous Linear Differential Equation
$a_{2} (x) y^{″} + a_{1} (x) y^{'} + a_{0} (x) y = 0 ⊛$
rewritten in standard form as
$y^{″} + P (x) y^{'} + Q (x) y = 0$

$x_{0}$ is an ordinary point of $⊛$ if $P (x)$ and $Q (x)$ are both analytic at $x_{0}$

If $x_{0}$ is not an ordinary point, it is called a singular point of $⊛$ .