power series solution about x0 =0 example 1

Introduction: In this question, we find power series solution about x0 =0 example 1 of an Ordinary differential equation. Step by step solution is given belowQuestion: Find power series solution about x0 =0 of differential equation\[\left(1+x^2\right)y^{\prime\prime}-xy^\prime+y=e^{-x}\]Solution:given differential equation\[\left(1+x^2\right)y^{\prime\prime}-xy^\prime+y=e^{-x} \] (1)…

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