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 June 30th, 2007, 09:55 AM #1 Newbie   Joined: Jun 2007 From: Milwaukee Posts: 11 Thanks: 0 Resolution of a differential system of equations I have a question in the following problem: Consider the system . . x = - y, y = -x (a) Sketch the vector field. (b) Show that the trajectories of the system are hyperbolas of the form x^2 - y^2 = C. (Hint: Show that the governing equations imply . . xx-yy = 0 and then integrate both sides.) ( c ) The origin is a saddle point; find equations for its stable and unstable manifolds. (d) The system can be decoupled and solved as follows. Introduce new variables u and v, where u = x + y, v = x – y. Then rewrite the system in terms of u and v. Solve for u(t) and v(t), starting from an arbitrary initial condition (u0, v0). (e) What are the equations for the stable and unstable manifolds in terms of u and v ? (f) Finally, using the answer to (d), write the general solution for x(t) and y(t), starting from an initial condition ( x0, y0 ). Tags differential, equations, resolution, system Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Norm850 Differential Equations 1 February 29th, 2012 03:26 PM brad66 Differential Equations 0 February 2nd, 2012 06:48 PM silentwf Differential Equations 2 January 4th, 2010 11:08 PM canicon25 Differential Equations 2 August 17th, 2009 03:16 PM Seng Peter Thao Differential Equations 0 June 30th, 2007 10:41 AM

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