Abstract <p>A mathematical study of a special class of boundary value problems on a segment with Dirichlet-type boundary conditions for a linear system of ordinary differential equations (ODE) with variable coefficients is carried out. These problems arise when calculating the output parameters of plasma in stationary plasma thruster (SPT) used to correct the orbits of spacecraft. The plasma was assumed to be incompressible with constant coefficients of conductivity, hydrodynamic viscosity and thermal conductivity of electrons and ions, and temperature relaxation. The ODE system under consideration is of the eighth order and theorems of existence and uniqueness of a solution are proved for the set boundary value problems, matrix Green’s functions are built, and two methods of successive approximations tending to a solution of the boundary value problem are presented.</p>