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?
