B. Consider the nonlinear system a' = y? – 1 y = x? – 4 i) Find all equilibrium solutions. (There are four.) ii) Linearize the system at each of the equilibrium points. Determine whether the...

Extracted text: B. Consider the nonlinear system a' = y? – 1 y = x? – 4 i) Find all equilibrium solutions. (There are four.) ii) Linearize the system at each of the equilibrium points. Determine whether the equilibrium point is hyperbolic or not. If it is hyperbolic, de- termine the whether the equilibrium is a source, sink or saddle. iii) Verify your findings by plotting the vector field using the vector field plotter we used on an earlier assignment. (Google 'vector field plotter' if necessary it's the first one.)