I am trying to solve the following PDE, subject to a highly unconventional boundary condition:
$$\frac{\partial p}{\partial x}=i m \frac{\partial^2 p}{\partial y^2}$$
$$\frac{\partial p}{\partial y} (x,0)=k \sqrt{x} p(x,0)$$ $$p(x,\infty)=1$$ $$p(0,y)=1$$
I tried using separation of variables, but the first boundary condition leads to a condition that can't be satisfied.
Does anyone know the trick or how to approach this exercise?