(a) Calculate [x (t)] 2 + [y(t)] 2 to show that the trajectories of the system x'...

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(a) Calculate [x (t)]2 + [y(t)]2 to show that the trajectories of the system x' = y, y' = -x of Problem 11 are circles. 

(b) Calculate [x (t)]2  - [y(t)]2 to show that the trajectories of the system x' = y, y' = x of Problem 12 are hyperbolas.

 Problem 11

x' = y, y' = -x

 Problem 12

x' = y, y' = x

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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