For the differential equation $\left(x^{2}-4\right)^{3}y''+\left(x-2\right)^{2}y'+y=0$
$x = -2$ is a ordinary point regular singular point irregular singular point
$x = 0$ is a ordinary point regular singular point irregular singular point
$x = 2$ is a ordinary point regular singular point irregular singular point

For this differential equation you would use a Taylor Frobenius series solution.