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4. Consider the differential equation (x2 + 1) y" + 4xy = 0. 80 (a) Without solving, if y(x) = an xn is used to solve this differential equation, is it possible to predict (with 100% certainty) that the n=0 solution will be a general solution? If yes, find the open interval of convergence of the general solution. If no, explain why the solution is not a general solution. 80 (b) Use y(x) = an xn to solve this differential equation. Write your solution in sigma notation and simplify as much as possible. n=0

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