Phase Plane, real unequal eigenvalues of the same sign

I have the following eigenvalues: r_1 = 4, r_2 = 2, which gives me the eigenvectors v_1 = [1, 1] and v_2 = [1,3] for r_1 and r_2 respectively. How should I draw the phase plane for this? This gives me two vectors that both approach infinity when t -> infinity? I've tried to find an example problem that draws the phase plane for this with no success. If anyone could either explain and/or point me to an example with this type of eigenvalues/vectors then that would be great. Thanks. :-)

Re: Phase Plane, real unequal eigenvalues of the same sign

First, draw the lines corresponding to the eigenvectors. If both eigenvectors are positive, this is a "source", if negative, a "sink". **Every** line through the equilibrium point is a solution. In order to show the difference in eigenvalues, one thing you can do is draw the lines **denser** (closer together) close to the eigenvector with larger eigenvalue, farther apart close to the eigenvector with smaller eigenvalue.

Re: Phase Plane, real unequal eigenvalues of the same sign

Quote:

Originally Posted by

**HallsofIvy** First, draw the lines corresponding to the eigenvectors. If both eigenvectors are positive, this is a "source", if negative, a "sink". **Every** line through the equilibrium point is a solution. In order to show the difference in eigenvalues, one thing you can do is draw the lines **denser** (closer together) close to the eigenvector with larger eigenvalue, farther apart close to the eigenvector with smaller eigenvalue.

Thank you for the input. However what I don't know how to do is how to draw the actual solutions, i.e. the lines that are drawn between the eigenvectors. What does it look like? Do you know what I could search for to find an example of how to do this?