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

Use the Fourier transform to find the solution in closed form. Feel free to look at tables of transforms.

$\displaystyle u(x,t) = {}$

help (formulas)