Solve the problem
PDE: $\quad u_t = u_{xx} - 6 u_x , \qquad -\infty < x < \infty , \quad t > 0$
IC: $\quad u(x,0) = 3 e^{-(x^2)/4}$

First, get rid of the convection term by changing variables, then use the Fourier transform.
$u = {}$

help (formulas)