Solution of Homogeneous and Inhomogeneous Linear differential Equations Systems Using Matrices

Abstract

The study addressed the solution of homogeneous and inhomogeneous linear differential equation systems using matrices. The systems of linear ordinary differential equations have important applications,possesspowerful tools in study and solvevarious problems in natural sciences, technology and social sciences. The matrices technique has been used in solving homogeneous and inhomogeneous linear differential equation systems by generating, eigevalues and eigenvectors of coefficient matrices along with many theories, definitions have been introduced in order to accelerate the process. It has been successfully implemented and found that, the method gives a typical results comparing with other analytical methods.However, the drawback of the scheme is the generating of eigenvalues, eigenvector and calculating matrices inverseare tedious and sophisticate when the order of coefficients matrices more than3 × 3.