Abstract

We consider canonical transformation for transforming scalar differential equations to matrix differential equations. We determine conditions for linear independence of solutions using the Wronskian method and use the Jordan canonical form to find bounds for solutions of ODES. Also considered are: the generalized eigenvectors method for obtaining matrix solutions to ODES and corresponding bounds for the autonomous differential equations, upper and lower bounds for solutions. Conditions for continuous dependence of solutions on initial data are formulated. Periodic systems are studied too with the application of the Floquet rule to finding solutions to some linear periodic systems. The Theorem on how to construct monodromy matrices is presented for the linear periodic systems together with some examples.