SOLUTION OF SOME SYSTEM OF LINEAR DIFFERENTIAL EQUATION USING MATRIX METHOD
Abstract
This project explores the solution of system of linear differential equations using the matrix method, a powerful and systematic approach in mathematical modelling. The method involves expressing the sysem in matrix form as dx dt = Ax+B, where A is the coefficient matrix, x is the state vector, and B represent external influences in nonhomogeneous cases. Solutions are obtained using eigenvalues and eigenvectors for diagonalizable systems, while the matrix represent exponential eAt is employed for general cases. The study demonstrates the effectiveness of the approach through examples, including homogeneous and non-homogeneous system. Applications in engineering, physics, and biological systems highlight the practical significance of the matrix method in solving complex dynamic models.
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