(a) Find the critical points of the plane autonomous system x' = 2xy y' = 1 -x2 + y2
Chapter 11, Problem 33(choose chapter or problem)
(a) Find the critical points of the plane autonomous system x' = 2xy y' = 1 -x2 + y2, and show that linearization gives no information about the nature of these critical points. (b) Use the phase-plane method to show that the critical points in part (a) are both centers. [Hint: Let u = y2/x, and show that (x - c)2 + y2 = c2 - 1.]
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