I have a problem when trying to solve this differential equation numerically which I thought would not be very difficult:
e_z''(x)+e_z (\text{x})=-e^{i x}\alpha (\text{x})
where
\alpha (\text{x})=\frac{-x+i}{x^2+1}
So I know that \alpha will go to zero as x goes to infinity or negative infinity so the solution for my e_z should be of the form e^{i x} in those limits.
How can I tell mathematica this when trying to use ndsolve because I have no other boundary conditions?