Determine if x0 = 0 is an ordinary or a singular point. If it is a singular point, determine if it is a regular or an irregular singular point.

Question

(2 + x) y'' + (1 + x) y' + 3y = 0

Answer 1

Write as y'' = (1+x)/(2+x) y' + 3/(2+x) y = 0

singular point is x = -2. x=0 is not singular. -2 is a a regular singular point because (2+x)*(1+x)/(2+x) converges.