Consider the equation $u_t = u_{xx} - 3 u_x$, $0 < x < 1$, $t > 0$, with boundary condition $u(0,t) = 0 , u(1,t) = 0$, and initial condition $u(x,0) = e^{1.5x}\!\left(6\sin\!\left(\pi x\right)+3\sin\!\left(2\pi x\right)+8\sin\!\left(3\pi x\right)\right)$. Solve.
$u(x,t) = {}$

help (formulas)