Question: 2. Consider the ODE in =y - x2+2, y = 212 - 2.xy. Find each fixed point and classify it according to linear stability analysis.

2. Consider the ODE in =y - x2+2, y = 212 - 2.xy. Find each fixed point and classify it according to linear stability analysis. Is it stable or unstable? Can the linear stability analysis be trusted? Indicate when it can and when it cannot be trusted. Additionally, identify the stable and unstable manifold (locally) for any saddle points. Finally, sketch (by hand, do not use any software such as pplane ) the local behavior of the phase diagram based off of the eigenvalues and eigenvectors at the fixed point. Label any basins of attraction or separatrices in this

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