1. Differential Equations MTH 242 Lecture # 28 Dr. Manshoor Ahmed

2. Summary(Recall) Initial value problem in case of system of differential equations. Existence and uniqueness theorem. Superposition principle. Linear independence and dependence. Wronskian in case system of equations. Complementary function and particular integral and general solution of a system of equations.

3. Most of the theory developed for a single linear differential equation can be extended to a system of such differential equations. The extension is not entirely obvious. However, using the notation and some ideas of matrix algebra discussed in a previous lecture most effectively carry it out. Therefore, in the present we will learn to solve the homogeneous linear systems of linear differential equations with real constant coefficients.

28. Case 3 Real and Repeated Eigenvalues

48. Exercises for practice

50. Summary Homogeneous system of linear DEs. Eigenvalue and Eigenvector. Solution of system when eigenvalues real and distinct. Solution of system when eigenvalues complex. Solution of system when eigenvalues real and repeated