Transient stability of power systems with de transmission is an important problem for planing and operation of future power networks. A differential-algebraic equation (DAE) system is proposed for transient stability analysis of a practical ac/dc power system which includes one synchronous generator operating onto both ac and dc transmissions. When transient stability analysis is performed using the DAE system, its solutions that represent dynamics of the ac/dc power system become discontinuous. This is because a constraint set, which is. a set of variables satisfying algebraic equations of the DAE system, discontinuously changes at the onset of fault occurrence and clearing. We numerically and analytically examine such discontinuous solutions of the DAE system and associated transient dynamics of the ac/dc power system. The discontinuous nature of solutions shows that enhancement of transient stability via dc transmission is characterized by a dynamical system on a constraint set or a manifold controlled by input as installation of dc transmission.