I am trying to find a general method to solve the following complex-valued , inhomogeneous second order differential equation $$ -a(x) u''(x)+b(x)u'(x)+c(x)u(x)+d(x)\bar{u}(x)=f(x),\quad x\in\mathbb{R}\tag{C-ODE}\label{ode}$$ where $a,$ $d,$ $c,$ $d$ are complex-valued functions.
As far as I know, if $d\equiv 0$ and if one knew a special solution to \eqref{ode} with $f\equiv 0,$ one can find general solutions to \eqref{ode} by using Wronskian and formula of variation of parameters.
However, I have no idea how to solve \eqref{ode} if $d\not\equiv 0.$ Can anyone give me some suggestions?