Consider the differential equation 2xy y x2 y 0 is the po

Consider the differential equation 2xy\" + y - x^(2) y = 0. is the point x = 0 an ordinary point, a regular singular point or irregular point ? if regular find indicial equations and the exponents at the singularity.

Solution

it not a regular point

because here p(x) is not differentible at x=0 and q(x) = 0 at x=0

p(x) = 1/2x    q(x) = -x/2

hence it is irregular point