Chapter 10.6, Problem 18E

In Problems 13 -18 , find the solution to the initial value problem:

$\begin{array}{l}\frac{{\partial }^{2}u}{\partial t^2}={\alpha }^2\frac{{\partial }^{2}u}{\partial x^2},-\infty <r<\infty ,t>0,\\ u\left(x,0\right)=f\left(x\right),-\infty <x<\infty ,\\ \frac{\partial u}{\partial t}\left(x,0\right)=g\left(x\right),-\infty <x<\infty ,\end{array}$

for the given function $f\left(x\right)$ and $g\left(x\right)$.

$f\left(x\right)=\cos 2x$, $g\left(x\right)=1-x$