Question: Complex ODE solutions using dsolve and fsolve.

I am currently trying to solve the following ODE using numerical methods:

diff(U(x), x$2) + [(z+ I*y)2/k12 -k22 + ((z+I*y)/k3)*sech(x)^2U(x)

Where the complex value (in this case, omega, has been written as z+Iy). I believe dsolve has capabilities for solving this as an initial value problem with complex values and thus to solve this as a boundary value problem I aim to use fsolve to find a zero other a function which is the (IVP solution) - (the non-initial boundary). This has worked very well for the case where y=0 however does not work for values of y>0, and it seems the problem is with fsolve. Any advice on how to deal with this problem, perhaps alternatives to fsolve? 

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