I am looking for the solution to the following Fokker-Planck equation.
$$\frac{\partial f(x,t)}{\partial t}= (k_1 x - v)\frac{\partial f(x,t)}{\partial x} + (k_2 x + D) \frac{\partial^2 f(x,t)}{\partial x^2},$$ where $k_1, v, k_2$ and $D$ are constants. In a domain $x \in (0, \infty)$. with boundary conditions that flux at $x=0$ is zero and $f(0,t)=0$ and initial condition, $f(1,0)=1$. The particle has an absorbing site at $x=\bar{x}$. In particular I want to find out the distribution of first passage time for this Fokker-Planck equation.