Chapter 10.2, Problem 24E

Find the formal solution to the vibrating string problem $\left(16\right)$- $\left(19\right)$ with $\alpha =4$, $L=\pi$ and the given and,

$\begin{array}{l}f\left(x\right)={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{n^2}\sin nx}\\ g\left(x\right)={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{{\left(-1\right)}^{n+1}}{n}\sin nx}\end{array}$