We wish to solve the problem
PDE: $\quad u_t = 9 u_{xx} - 6 u_x , \qquad -\infty < x < \infty , \quad t > 0$
IC: $\quad u(x,0) = 9 + 8 \cos( x ) + \sin(\pi x)$

First we change variables to $\xi = x- 6 t, \tau = t$. The solution in terms of $\xi$ and $\tau$ (type "xi" and "tau" for the variables) is:
$u = {}$

The solution in terms of $x$ and $t$ then is
$u = {}$

help (formulas)