MATH 2341 Study Guide - Quiz Guide: Equilibrium Point, Phase Portrait

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2341
• Professor: All

Document Summary

Quiz 3: 8 points consider the linear system x = ax, with a = (cid:18)2 3. Spring 2013: 7 points the matrix a = (cid:18) 7. 4 1(cid:19) has eigenvalues 1 = 3 and 2 = 5, with corresponding. Sketch the phase portrait for the linear system. X = ax, indicating the straight-line solutions, and at least 4 other solution curves. Spring 2013: 7 points consider the linear system x = ax, with a = (cid:18)0 4. 4 (a) find the general solution x = x(t). (b) find the solution x = x(t) with initial condition x(0) = (cid:18)1. 1(cid:19). (c) sketch the x(t)- and y(t)-graphs of this particular solution. Spring 2013: 8 points consider the linear system x = ax, with a = (cid:18) 6 2. What is limt x(t) in this case? (e) sketch the phase portrait for the system, making sure you indicate the particular solution found in part (d).