Systems of ODEs - Sources and Sinks

Explore 2-dimensional linear systems of ordinary differential equations with pairs of positive or negative real eigenvalues in this 25-minute video lecture. Investigate unstable sources and stable sinks through eigenvalue and eigenvector analysis, as well as phase portrait visualizations. Learn to write solutions, compute matrix inverses, and draw both unstable sources and stable sinks in phase space. Gain insights into the behavior of these systems and their applications in various fields of science and engineering.

Overview of sources and sinks
Writing the solution
Recap: How to compute matrix inverse
Drawing an unstable source in phase space
Drawing a stable sink in phase space