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Consider the following autonomous differential equation, dN = -a N – N2 dt where a > 0. It is clear that N = 0 and N this differential equation? = -a are the two distinct equilibria of this differential equation. What can you conclude about the equilibria of ON=0 and N =-a are locally stable. ON=0 is locally stable and N = -a is unstable. ON=0 and N a are unstable. ON- = 0 is unstable and N =-a is locally stable. There is not enough information to answer this question.

Consider the following autonomous differential equation, dN = -a N – N2 dt where a > 0. It is clear that N = 0 and N this differential equation? = -a are the two distinct equilibria of this differential equation. What can you conclude about the equilibria of ON=0 and N =-a are locally stable. ON=0 is locally stable and N = -a is unstable. ON=0 and N a are unstable. ON- = 0 is unstable and N =-a is locally stable. There is not enough information to answer this question.

Advanced Engineering Mathematics
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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Consider the following autonomous differential equation, NP = -aN- N2 dt where a > 0. It is clear that N = 0 andN= -a are the two distinct equilibria of this differential equation. What can you conclude about the equilibria of this differential equation? ON=0 and N =-a are locally stable. ON=0 is locally stable and N =-a is unstable. ON=0 and N =-a are unstable. ON=0 is unstable and N =-a is locally stable. O There is not enough information to answer this question.
Transcribed Image Text:Consider the following autonomous differential equation, NP = -aN- N2 dt where a > 0. It is clear that N = 0 andN= -a are the two distinct equilibria of this differential equation. What can you conclude about the equilibria of this differential equation? ON=0 and N =-a are locally stable. ON=0 is locally stable and N =-a is unstable. ON=0 and N =-a are unstable. ON=0 is unstable and N =-a is locally stable. O There is not enough information to answer this question.
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