What I will do is use implicit differentiation to see if you can separate the variables so that they can be calculated independent of each other.
d/dx(Ax - xe^(By)) = d/dx(y)
= A - d/dx(xe^(By))
= A - [e^(By) + Bx*e^(By)dy/dx] So this implies:
dy/dx[1 + Bxe^(By)] = A - e^(By) or
dy/dx = [A - e^(By)]/[1 + Bxe^(By)]
This looks like all derivatives will involve x's and y's which means that you can't get y as a function purely of x (or the other way around unless you use specific restrictions or find a parameterization.