Problems For the following systems, draw a direction field and plot some representative trajectories. Using your graph, give the type and stability of the origin as a critical point. You may need to look at the eigenvalues to be sure. 1. -2 x, c, x'= -5 4 \22 2. For the system ax x(2-x-y), dt Find all the critical points (equilibrium solutions). Draw a direction field and a phase portrait of representative trajectories for the system. Caution: You'll need to change the ode45 statement to go over the interval [0,2] instead of -10,10] or else you'll get a bunch of accuracy errors. This may be necessary in other problems as well.) a. b. c. From the plot, discuss the stability of each critical point and classify it as to type. For the system 3. a. Find all the critical points (equilibrium solutions). b. Find the corresponding linear system near each critical point. c. Find the eigenvalues of each linear system. Using Table 9.3.1 classify the type and stabilit each critical point based on the eigenvalues Draw a direction field and phase portrait of the nonlinear system. Does this confirm or provide additional information to your answers in part c? d