We want to solve the problem
PDE: $\quad u_{t} = 9 u_{xx} , \qquad 0 < x < 6 , \quad t > 0$
BC: $\quad u(0,t) = 8 \quad u(6,t) = 9$
IC: $\quad u(x,0) = 0$
And we have the solution of the problem
PDE: $\quad v_{\tau} = v_{\xi\xi} , \qquad 0 < \xi < 1 , \quad \tau > 0$
BC: $\quad v(0,\tau) = 0 \quad v(1,\tau) = 1$
IC: $\quad v(\xi,0) = 0$

Write $u(x,t)$ in terms of $v(\xi,\tau)$
$u(x,t) = {}$

help (formulas)