Solving the overdetermined problems for systems of linear ordinary differential equations

The ways of applying the least squares method for solving the overdetermined systems of linear ordinary differential equations with possibly redundant boundary conditions are considered. Such problems generally have no solutions.
The methods proposed for solving these problems take into account both the equations themselves and the corresponding boundary conditions. In one of these methods the order of equations of the considered system is increased. In this case additional boundary conditions are formulated for the system. The model examples of application of the methods and their comparison are given.