Explore more examples of second-order Ordinary Differential Equations and their solutions in this 32-minute video lecture. Review the characteristic polynomial and learn how to apply initial conditions. Discover the relationship between eigenvalues of the matrix system and roots of the characteristic polynomial. Follow along with practical examples, including writing equations as matrix systems and using MATLAB to plot and integrate solutions. Examine both stable and unstable systems through multiple examples, enhancing your understanding of differential equations and their applications.