We consider transfer functions of linear time-invariant differential-algebraic systems. Based on the stabilizing solutions of certain differential-algebraic Lur'e equations, we will derive simple formulas for realizations of inner-outer factorizations. We show that the existence of a stabilizing solution only requires behavioral stabilizability of the system. We neither assume properness nor (proper) invertibility of the transfer function. We briefly discuss numerical aspects for the determination of such factorizations.