Phase Portrait of Linear ODE Systems with Imaginary Eigenvalues

This GeoGebra example demonstrates the phase portrait of a linear system of differential equations with constant coefficients when the coefficient matrix has two imaginary eigenvalues. It visualizes trajectories around an equilibrium point, typically closed orbits for a center, and connects eigenvalues, eigenvectors, stability, and phase-plane analysis. The construction uses the SolveODE command to solve the differential equations, numericalIntegral1 through numericalIntegral8 to generate or support trajectory-related computations, objects such as a, g, A, f, B, C, D, E, F, G, and H to organize parameters and key points, and text1 through text4 for annotations. It is suitable for undergraduate differential equations, linear algebra, dynamical systems, and mathematical modeling courses.