Using stochastic(!) methods find explicit solution to each of the two ($i = 1, 2$) initial value problems $\partial_t u(t, x) = \frac{1}{2} \beta^2 \partial_x^ 2 u(t, x) + (−\alpha x + \gamma )\partial_x u(t, x)$
with $u(0, x) = f_i(x)$ where $f_1 (x) = \delta(x)$ is the Dirac function and $f_2 (x) = x$.