power series

[logistic_guy]

\(\displaystyle \textcolor{indigo}{\bold{Solve.}}\)

\(\displaystyle y'' + y = 0\)

 

[logistic_guy]

To warm up the audience, we write the form of \(\displaystyle y\) as a power series.

\(\displaystyle y = \sum_{n=0}^{\infty}a_nx^n\)

 

[logistic_guy]

\(\displaystyle y' = \sum_{n=0}^{\infty}a_nnx^{n-1}\)