Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrödinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.