Using the cosine transform solve
PDE: $\quad u_{t} = 9 u_{xx}, \quad 0 < x < 1$ and $t > 0$.
BC: $\quad u_x(0,t) = u_x(1,t) = 0$
IC: $\quad u(x,0) = 6 + 8 \cos(\pi x) + 9 \cos(2\pi x)$

Solve: $u(x,t) = {}$

Based on this solution what is the steady state, that is what is $\lim_{t\to \infty} u(x,t) = {}$

help (formulas)