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I've just started learning to solve DE by using power series and I am not sure If I did it the right way. Would anybody be kind enough going thru my solution here and see if I did it right? I want to make sure I am doing the right thing, I am very bad with series. Thanks in advance!

and i have another problem : xy' = y^2 +x^2, how do I solve it? I do not know how to deal with the y^2 .

and i have another problem : xy' = y^2 +x^2, how do I solve it? I do not know how to deal with the y^2 .

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