# Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients

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Lesson Summary:

In this lesson, we learn how to sketch the solutions of a 2x2 homogeneous linear system with constant coefficients by modeling a sublimated war between two states. We start by solving the equations using a standard technique and then plotting the four easy solutions (pink, orange, blue, and green) that correspond to the normal modes. From there, we use the fact that the velocity field corresponding to the system of differential equations changes continuously to deduce that all trajectories are coming to the origin, but not necessarily in straight lines. This is an important skill to have when studying nonlinear equations.

Lesson Description:

Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients -- Lecture 27. Learn what graphs of systems of differential equations look like.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 28, 2008). License: Creative Commons BY-NC-SA.
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