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Solve differential equation using power series

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Solve differential equation using power / Taylor series. Need problems 2,4,6,8,10.
See attached file for full problem description.
2. y' = xy
4. (x- 3)y' + 2y = 0
6. y'' = y
8. y'' = xy
10. y'' + x^2y = 0, y(0) = 1, y'(0) = 0.

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