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Differential EquationsEasySeries Solutions

Series Solutions · Easy problem

Solve y′′=2y′−x yy'' = 2y' - x\,y with y(0)=1y(0) = 1, y′(0)=1y'(0) = 1 by a power series y=∑n=0∞anxny = \sum_{n=0}^{\infty} a_n x^n. Find a3a_3. Express your answer as a common fraction.