Phase Portrait of a Linear System of Differential Equations

Use nullclines to sketch the phase portrait in the phase plane for the linear system dx/dt = -2x-2y, dy/dt = -x-3y. The equilibrium point at the origin is a sink. Straight line solutions are inferred from the rest of the phase portrait. DSolveValue and MatrixExp can confirm the solutions with Mathematica, based on the unique solution of dY/dt = A*Y, Y(0)=Y0 being Y=e^(At)*Y0, where e^(At) is the matrix exponential of the matrix At = tA (t is a scalar and A is a matrix). Differential Equations, 4th Edition (by Blanchard, Devaney, and Hall): https://amzn.to/35Wxabr. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: https://twitter.com/billkinneymath 🔴 Follow me on Instagram: https://www.instagram.com/billkinneymath/ 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ ⏱️TIMESTAMPS⏱️ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.