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###### Exercise 8.2.52: For the systems below:Find all critical points (equilibria).Determine the linearized systemt for each Of the points in (i.). Classify each of the critical points (equilibria) . If the critical points are not . spirals or centers, find all eigenvectors: Sketch the global phase portrait. Include the eigenvectors for the linearized system at each critical point and draw arrows n the solution curves to indicate the direction of flow: x' =x-xty,y = 212_8.2 STABILITY AND CLASSIF

Exercise 8.2.52: For the systems below: Find all critical points (equilibria). Determine the linearized systemt for each Of the points in (i.). Classify each of the critical points (equilibria) . If the critical points are not . spirals or centers, find all eigenvectors: Sketch the global phase portrait. Include the eigenvectors for the linearized system at each critical point and draw arrows n the solution curves to indicate the direction of flow: x' =x-xty,y = 212_ 8.2 STABILITY AND CLASSIFICATION OF ISOLATED CRITICAL POINTS 277 b) x' = -3x+y,y' =-y+x2 c) x' =-x+y?,y' =x+2y d) x' = 2x+ y,y' = ~y+x2

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