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Consider the system i = -y, = -x. (a) Sketch the vector field (phase portrait). (b) Show that the trajectories of the system are

 

Consider the system i = -y, = -x. (a) Sketch the vector field (phase portrait). (b) Show that the trajectories of the system are hyperbolas of the form x2 y? = C. (Hint: first show that ix yy = 0.) (c) The origin is a saddle point. Find equations for its stable and unstable manifolds.

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