Question: Consider the differential equation xy+ y' 2y= 0, 2: > 0, which has a regular singular point at 220 = 0- (a) Determine the indicial

$Consider the differential equation xy\"+ y' 2y= 0, 2: > 0,$

Consider the differential equation xy\"+ y' 2y= 0, 2: > 0, which has a regular singular point at 220 = 0- (a) Determine the indicial equation, roots of the indicial equation, and recurrence relation corresponding to a series solution about .120 = 0. (b) The rst solution 191(3) is given by (you do not need to show this). Show that the second linearly independent solution takes the form: y2(a:) = (lnz)y1(x) 4m 3:1:2 + .. .. You should explain your working

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