Use Nullclines to Sketch the Phase Portrait for a Linear System of ODEs, Solve w/ Matrix Exponential

Consider the linear system of ordinary differential equations dx/dt = x' = -2x - 2y, dy/dt = y' = -x - 3y. The x-nullcline (where dx/dt = 0 and the vector field is vertical) is the line y = -x, and the y-nullcline (where dy/dt = 0 and the vector field is horizontal) is the line y = -x/3. The directions of solutions between nullclines is analyzed, solutions are drawn, and we infer the existence of straight-line solutions. In matrix/vector form, the solution is written using the matrix exponential e^(tA), and MatrixExp on Wolfram Mathematica is used to find it. Differential Equations, 4th Edition (by Blanchard, Devaney, and Hall): amzn.to/35Wxabr.
Differential Equations and Linear Algebra Course Playlist: • Differential Equations...
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