I am trying to solve the following Fokker Planck PDE: $$ \dfrac{\partial u(t,x)}{\partial t} = -\dfrac{\partial u(t,x)}{\partial x} + \dfrac{1}{2}\dfrac{\partial^2 }{\partial x^2}[ 3 x^2 u(t,x)]. $$
Can't figure out a way (transformation of $x$) to reduce it to the basic $u_t=0.5 u_{xx}$ or anything with a known solution for that matter. Would appreciate any help. Thanks in advance.
