Question

(Singular Points) (a) Classify the singular points of the differential equation (22 – 1)?y" + (x + 1)y' – y = 0. (b) Determine the indicial equation for the regular singular point(s) found in part (a). Also find the corresponding exponents of the singularity for those points.

Answer 1

solo) (x²_179" +(x+1) 9'-y=0 y" + (at) y' y (x2-1) 2 درمور ) x+1 so let p(x)= (x+1/² (x-1) (x+1) (2-1, 2 1 and 900) = (x2-1) (x+1)2(x-132 So, equation has two singular points x = 1 and x = -1 we see for 1 Lim x-1 and (2+1) Lim (xup (x) xx-i (x+1) (2-172 % Lim (2-13 Q(x) = Lim - (x-13² and (2+1)2(x-132 indicial equation ele-1) + pore +9 = 0 x y1 اس پر then the 1 e 42 4 O 4 & ²3r-1=0 U 42 u 4 3 + √9 - 4(4) (-1) 375 2xy 3-5 3+5 L, and - are I and So, value of e I 4