Transform the problem
PDE: $\quad u_{tt} = 9 u_{xx} , \qquad 0 < x < 6 , \quad t > 0$
BC: $\quad u(0,t) = 8 \quad u(6,t) = 9$
IC: $\quad u(x,0) = x^2, \quad u_t(x,0) = x^3$
into a dimensionless problem:
PDE: $\quad U_{\tau\tau} = U_{\xi\xi} , \qquad 0 < \xi < 1 , \quad \tau > 0$
BC: $\quad U(0,\tau) = 0 \quad u(1,\tau) = 1$
IC: $\quad U(\xi,0) = {}$
$\quad U_{\tau}(\xi,0) = {}$
Type xi, tau for the variables. (You might want to first figure out the answers below)

First, you transform u to U. Use just small "u" instead of "u(x,t)":
$U = {}$

Next, transform $x$ to $\xi$.
$\xi = {}$

Finally, transform $t$ to $\tau$.
$\tau = {}$

help (formulas)