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Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y = 0 a) Show that...

Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y = 0

a) Show that x = 0 is a regular singular point for the equation.

b) For a series solution of the form y = ∑∞ n=0 an x^(n+r)   a0 ̸= 0 of the differential equation about x = 0, find a recurrence relation that defines the coefficients an’s corresponding to the larger root of the indicial equation. Do not solve the recurrence relation.

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