The differential equations linear homogeneous system solutions investigation

The paper shows that the fundamental zero-normalized solution of a linear homogeneous differential equations system can be represented as an exponential matrices products formal series. If the system satisfies the equations system triangulation Perron theorem conditions, then the system solution can be represented as an exponential matrices finite product. In addition, an exponential matrix function differentiating formula is derived. Also, the transformation constructing problem is considered. Such, a homogeneous differential equations system allows to reduce to a triangular form.