The apparatus of the non-holonomic mechanics developed for deriving of the motion equations for the systems with the higher order constraints is applied for the solution of the combined problems of dynamics. In combined problems the system moves under the given system of active forces satisfying the program of the motion. This program is written on the form of an additional system of differential equation of the higher order (the higher order constraints). The control forces (the generalized higher order constraints) are treated as auxiliary unknown functions in time. To obtain the generalized coordinates and control forces the joint system of differential equations is constructed. The proposed theory is illustrated with the example of the motion of a spaceship the acceleration of which is constant in modulus since some moment of time. This condition is treated as a non-linear non-holonomic constrain of the second order.