Question: Part c got cropped out. c. Classify each equilibrium solution. Is each stable or unstable? If either equilibrium solution is a center for the linear

Part c got cropped out. c. Classify each equilibrium solution. Is each stable or unstable? If either equilibrium solution is a center for the linear system, will it definitely be a center in the nonlinear system? If not, what are the other possibilities?

10. (8 points) Consider the system x'=y(y3) y'=x a. Find all equilibrium solutions [critical points. b. Find the corresponding linear system near each equilibrium solution (by using the formal approach with the lacobian matrix)

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