MathCastle
Differential EquationsMediumSeries Solutions

Series Solutions · Medium problem

Solve y′′+x y=0y'' + x\,y = 0 with y(1)=1y(1) = 1, y′(1)=0y'(1) = 0 by a power series about x0=1x_0 = 1, y=∑n=0∞bn(x−1)ny = \sum_{n=0}^{\infty} b_n (x-1)^n. Find b3b_3. Express your answer as a common fraction.