Note that x = 0 is an irregular point of the equation x2y″ + (3x − 1)y′ + y = 0.
(a) Show that y = xr Σ cnxn can satisfy this equation only if r = 0. (b) Substitute y = Σ cnxn to derive the “formal” solution y = Σ n!xn. What is the radius of convergence of this series?
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