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Question 4 . For the following two initial value problems, we cannot guarantee that a power series solution centered at x = 0 exists since

Question 4. For the following two initial value problems, we cannot guarantee that a power series solution centered at x=0 exists since x=0 is not a regular point. However, in some cases, we may still be able to find one anyway, even if we can't guarantee it will work beforehand.
(i)xy''y=0,y(0)=1,y'(0)=0
(ii)x2y''-2xy'2y=0,y(0)=0,y'(0)=2
For one of the above equations, we can still find a solution esing power series centered at x=0, and for the other we cannot. Which is which?
Question 4 . For the following two initial value

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