I keep getting stuck after the reindexing, Power Series. as well as using their solutions to prove they are correct, Use power series to solve the initial-value problem (x² – 3)y" + 6xy + 4y = 0 ,...

I keep getting stuck after the reindexing, Power Series. as well as using their solutions to prove they are correct,

Extracted text: Use power series to solve the initial-value problem (x² – 3)y" + 6xy + 4y = 0 , У(0) — 1, y'(0) = 0. - Σ Answer: y 2n + 2n+1 n=0 n=0


Extracted text: Use power series to solve the initial-value problem y" + 2xy' + 4y = 0 , y(0) = 0, y (0) = 1. Answer: y = x2n + r2n+1 n=0 n=0