how to Apply power series method to solve y’’-xy=x

Question : Apply power series method to solve y’’-xy=x Solution: We shall Apply power series method to solve y’’-xy=x Given ode \[y^{\prime\prime}-xy=x\] (1) Let power series \[y=\sum_{n=0}^{\infty}{a_nx^n} \] Is a solution of eqn (1) Differentiating eqn (1) \[\Rightarrow y^\prime=\sum_{n=1}^{\infty}{na_nx^{n-1}\ \…

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