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Differential EquationsEasySeries Solutions

Series Solutions · Easy problem

Solve (1−x) y′=y(1 - x)\,y' = y with y(0)=1y(0) = 1 by a power series y=∑n=0∞anxny = \sum_{n=0}^{\infty} a_n x^n. Find the sum of this series at x=13x = \dfrac13. Express your answer as a common fraction.