Question: Class Assignment 6 Problem. (a) Use the power series method to solve the differential equation 00 0 y (x) xy (x) + x3 y(x) =

Class Assignment 6 Problem. (a) Use the power series method to solve the differential equation 00 0 y (x) xy (x) + x3 y(x) = 0 . Write the first 5 non-vanishing terms of the power series solutions. (b) Determine a real interval where the power series solutions will be convergent and explain why on this interval the power series solutions will be convergent. Hints: 1. Choose an appropriate point as a center of the power series solution and explain why we can solve the given differential equation in terms of power series about this point (centered at this point). 2. You have to find a fundamental set of solutions in terms of power series about the appropriately chosen point (centered at the appropriately chosen point). Then, construct the general solution. 1

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