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AsymptoticDSolveValue[2x*y''[x] -(3+2x)*y[x] +1 == 0, y[x], {x, 0, 5}], this differential equation command, is not outputting the correct solution. The solution should be like y=C1(1+(1/3)x-(1/6)x^2-(1/6)x^3+...)+ C2 x^(5/2) (1+(4/7)x + (4/21)x^2+...)this but the output from mathematical is different. Could you help me with what to type for the command in order to output the correct series solution? Thank you!

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1 Answer 1

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If the problem is the grouping of the terms, use Collect

$Version

(* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *)

Clear["Global`*"]

eqn = 2 x*y''[x] - (3 + 2 x)*y[x] + 1 == 0;

(sol = (AsymptoticDSolveValue[eqn, y[x], {x, 0, 5}] //
     FullSimplify // Collect[#, {C[1], C[2], x}] &))

enter image description here

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