So I want to be able to draw the phase portrait for linear systems such as: x'=x-2y y'=3x-4y I am completely confused, but this is what I have come up with so far: Step 1: Write out the system in the form of a matrix. Step 2: Find the eigenvalues and eigenvectors for the matrix. Step 3: Using the eigenvectors draw the eigenlines. Step 4: Using the the eigenvalues label the direction of the eigenlines[(+) = away, (-)= towards] Step 5: Using the eigenvalues determine the type of the system. Eg: node, star, spiral etc. Step 6: Fill in a few trajectories. My issues appear at steps 5 and 6, I can't figure out how to draw the trajectories. Which eigenline should they be based around ? Also with complex eigenvalues or when there is 1 eigenvector what do I have to do ? Any help or link to a webpage would be greatly appreciated.