(a) Beginning with the general solution of the systemx' = -2y, y' = 2x , calculate x2 + y2 to show that the trajectories are circles. (b) Show similarly that the trajectories of the system x' = 1/2y, y' = -8x are ellipses with equations of the form 16x2 + y2 =C2.
(a) Beginning with the general solution of the systemx' = -2y, y' = 2x , calculate x2 + y2 to show that the trajectories are circles. (b) Show similarly that the trajectories of the system x' = 1/2y, y' = -8x are ellipses with equations of the form 16x2 + y2 =C2.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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(a) Beginning with the general solution of the system
x' = -2y, y' = 2x , calculate x2 + y2 to show that the trajectories are
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