How does one derive the general solution to this ODE ( is a constant)?
Well, one problem you have is that this is NOT an "ODE"! Since P is a function of two variables, and your equation involves derivatives with respect to both, that is a partial differential equation
But I am puzzled as to where you got this problem. Are you not taking a class in partial differential equations? If you are, then you should have encountered the "method of characteristics".