GSW Problem Set 6

GSW Problem Set 6 - → ∞ 2 Consider the system x = y 2(3...

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EA 4 Workshop questions - week of 11/17/08 1. Consider the system x 0 = x 2 + y 2 , (1) y 0 = x 2 + y 2 . (2) (a) Determine all critical points for system (1). (b) How does this critical point differ from those discussed in class? (c) Determine an equation for the trajectories of this system. (d) Consider the solution with the initial condition x (0) = - 1 , y (0) = - 2 . Determine the trajectory of the solution and the limits of x ( t ) and y ( t ) as t t * , where t * is the upper limit of times for which the solution exists (will be Fnite). (e) Consider the solution with the initial condition x (0) = y (0) = - 1 . Determine the limits of x ( t ) and y ( t ) as t
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Unformatted text preview: → ∞ . 2. Consider the system x = y 2 , (3) y = x 2 . (4) (a) Determine all critical points of system (3). (b) Determine the trajectories of system (3). (c) Determine the behavior of all solutions. In particular, determine the difference in be-havior between the solution with x (0) = y (0) =-1000 and the solution with x (0) =-1000 , y (0) =-1000 . 00001 3. Give an example of a linear system where the origin is a center and the trajectories are circles which are traversed in the counter-clockwise direction....
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This note was uploaded on 09/08/2010 for the course GEN_ENG 205 taught by Professor Taflove during the Spring '08 term at Northwestern.

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