I have come across an equation of the following form $\frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}(y-x)^{2}}[C_{1}x+C_{2}y+C_{3}x^{2}y + C_{3}y^{2}x] = C_{4}xy$ where $C_{j}$ are real-valued constants. I'd like to be able to solve for $x$ in closed form, in terms of $y$ and the $C_{j}$. Alternately, I would also like to show the following result (which I am not sure holds): given $C_{1}
Edit: I mean the constants to be arbitrary except for the one restriction mentioned, so I am looking for a general solution in that sense.