Question

Solve using power series.
y" + 4y = 0

Answer 1

supose solution y can be written as series:
\[y=\Sigma_{n=0}^{\infty}a_{n}x^n\]
find it's 2º derivative and substitute in the equation:
\[\Sigma n(n-1)a_{n}x^{n-2}+4\Sigma a_{n}x^{n}=0\]
Now equalize the sumation indexes and express a_n recursive way