Linearization. Consider the systemEnter the system in pplane6.a) Find the equilibrium poin...

Linearization. Consider the system

Enter the system in pplane6.

a) Find the equilibrium point at (1/2, 3/2). Display the linearization, plot the stable and unstable orbits and several solution trajectories to create a phase portrait of the linearization.

b) Return to the PPLANE6 Display window. Select Edit→Zoom in square, place the mouse at the equilibrium point (1/2,3/2), then drag and release a small zoom box. On a PC, you can depress the shift key, then drag with the left mouse button to achieve the same effect. Repeat several times until you have zoomed sufficiently close to the equilibrium point. Plot the stable and unstable orbits and several trajectories to create a phase portrait of the nonlinear system near (1/2, 3/2). Compare this phase portrait with the phase portrait in the linearization window.