Question: 2. Let a, b E R. Consider the differential equation: xu + (b - x)u - au = 0. (a) Show that a power series

2. Let a, b E R. Consider the differential equation: xu" + (b - x)u - au = 0. (a) Show that a power series solution of Eq. (1) is a u(a, b; a) = 1+ a(a + 1) x2 - ac + a(at 1) . . . (atn-1)x b b (b + 1) 2! + ... + b ( b + 1 ) . . . ( b t n - 1) n! + ... (b) Show that u(a, b, x) has a radius of convergence R = 00

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