(1) By analyzing the singular points of the differential equation, we know that a series solution of the form for the differential equation will converge at least on the interval .
(2) Substituting into , you get that
(3) In this step we will use the equation above to solve for some of the terms in the series and find the recurrence relation. (a) From the constant term in the series above, we know that
(4) The general solution to converges at least on and is (5) Solve the initial value problem
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