Question

xy', + y,-xy = 0, x,-0 Answer the following questions a) What are the points of singularity for each specific problem? b) Does this ODE hold a general power series solution at the specific x0? Justify your answer, i) if your answer is yes, the proceed as follows: Compute the radius of analyticity and report the corresponding interval, and ldentify the recursion formula for the power series coefficient around x0, and write the corresponding solution with at least four non-zero terms explicitly written ii) If your answer is no, then please elaborate why there is not a general power series solution, and proceed to solve it using the Frobenius method

Answer 1

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(K+2) 2 (k-2 )2(K+4)2 22 22, 42 a Second Solutiom 1s(aywhoe Y k u) gives 2 -2 (K+2) 3 d gzepacino Coby b Ir⑥gues putting K=o, an OK 22 22. 42 -b/a Log χ.tf-z?.--. _c (It2)-1-bV The Sue?"ルoed Solution is y=au+bv