MathCastle
Differential EquationsEasySeries Solutions

Series Solutions · Easy problem

Solve y′′=x y′+yy'' = x\,y' + y with y(0)=1y(0) = 1, y′(0)=2y'(0) = 2 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.