5. Consider the autonomous system dr -y" – (3 + 1)x"y® – 1 dy z" +az"-'y+1 + y, dt n,m, a, 3 2 3. a.) Find first integral and integral manifold of the system. b.) Can we use Morse theorem to decide about the nature of the origin? Explain your answer.

5. Consider the autonomous system dr -y" – (3 + 1)x"y® – 1 dy z" +az"-'y+1 + y, dt n,m, a, 3 2 3. a.) Find first integral and integral manifold of the system. b.) Can we use Morse theorem to decide about the nature of the origin? Explain your answer.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter7: Locus And Concurrence

Section7.2: Concurrence Of Lines

Problem 7E: Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a...

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5. Consider the autonomous system
da
= -y" – (3+ 1)x®y® – :
dt
dy
= r" + ar"-1
dt
+ y,
п, т, а, В 2 3.
a.) Find first integral and integral manifold of the system.
b.) Can we use Morse theorem to decide about the nature of the origin? Explain your
answer.

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