Investigate the type of the critical point (0,0) of the given almost linear system. dx = - 2x-2y +x3 dy =x-4y+y dt V of the linearized system. The eigenvalue(s) of the associated linear system, i=. are complex-valued with a negative real part. (Simplify your answer. Use a comma to separate answers as needed. Type each solution only once. Type an exact answer, using radicals Thus, the critical point (0,0) is From the above step and the Stability of Almost Linear Systems Theorem, which of the following statements can be concluded about the t asymptotically stable proper node or improper node O A. The critical point (0,0) is an asymptotically stable spiral point. O B. The critical point (0,0) is either a either a center or a spiral point, and it may be either asymptotically stable, stable, or unstable. unstable proper node or improper node OC. The critical point (0,0) is either a node or a spiral point, and it is unstable. unstable saddle point O D. The critical point (0,0) is either a node or a spiral point, and it is asymptotically stable. unstable spiral point asymptotically stable spiral point stable center unstable improper node asymptotically stable improper node
Investigate the type of the critical point (0,0) of the given almost linear system. dx = - 2x-2y +x3 dy =x-4y+y dt V of the linearized system. The eigenvalue(s) of the associated linear system, i=. are complex-valued with a negative real part. (Simplify your answer. Use a comma to separate answers as needed. Type each solution only once. Type an exact answer, using radicals Thus, the critical point (0,0) is From the above step and the Stability of Almost Linear Systems Theorem, which of the following statements can be concluded about the t asymptotically stable proper node or improper node O A. The critical point (0,0) is an asymptotically stable spiral point. O B. The critical point (0,0) is either a either a center or a spiral point, and it may be either asymptotically stable, stable, or unstable. unstable proper node or improper node OC. The critical point (0,0) is either a node or a spiral point, and it is unstable. unstable saddle point O D. The critical point (0,0) is either a node or a spiral point, and it is asymptotically stable. unstable spiral point asymptotically stable spiral point stable center unstable improper node asymptotically stable improper node
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Investigate the type of the critical point (0,0) of the given almost linear system.
dx
- - 2x - 2y + x
dt
dy
=x-4y +y
dt
...
The eigenvalue(s) of the associated linear system, À =. are complex-valued with a negative real part.
Thus, the critical point (0,0) is
of the linearized system.
(Simplify your answer. Use a comma to separate answers as needed. Type each solution only once. Type an exact answer, using radicals
From the above step and the Stability of Almost Linear Systems Theorem, which of the following statements can be concluded about the t
asymptotically stable proper node or improper node
O A. The critical point (0,0) is an asymptotically stable spiral point.
O B. The critical point (0,0) is either a either a center or a spiral point, and it may be either asymptotically stable, stable, or unstable.
unstable proper node or improper node
OC. The critical point (0,0) is either a node or a spiral point, and it is unstable.
unstable saddle point
O D. The critical point (0,0) i
either a node or a spiral point, and it is asymptotically stable.
unstable spiral point
asymptotically stable spiral point
stable center
unstable improper node
asymptotically stable improper node
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