Chapter 10.5, Problem 1E

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

$\frac{\partial u}{\partial t}=5\frac{{\partial }^{2}u}{\partial x^2}$, $0<x<1$, $t>0$,

$u\left(0,t\right)=u\left(1,t\right)=0$, $t>0,$

$u\left(x,0\right)=\left(1-x\right)x^2$, $0<x<1$