Chapter 10.5, Problem 6E

In Problems 1 -10 , find a formal solution to the given initial boundary value problem.

$\frac{\partial u}{\partial t}=7\frac{{\partial }^{2}u}{\partial x^2},0<x<\pi ,t>0$,

$\frac{\partial u}{\partial x}\left(0,t\right)=\frac{\partial u}{\partial x}\left(\pi ,t\right)=0\text{,}t>0$,

$u\left(x,0\right)=1-\sin x,0<x<\pi$