System of Linear DEs Real Repeated Eigenvalues #1
Shown below is the phase portrait for a linear system of differential equations with constant coefficients and two real, equal (repeated) eigenvalues. Here, the derivatives are with respect to time, and we are interested in the behavior of the solutions to the differential equation as time increases from zero.
Each solution to the differential equation is called a trajectory. The initial values (at t = 0) of each solution are shown as points (red dots) in the phase plane (the xy-plane).
Try dragging the initial value points closer to and further from the eigenvector (shown as a green line).
Do the solutions move toward the origin or away from it?
Why do you think the origin is called an unstable node in this phase portrait?