Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![1. Find all steady states of differential equationx5x24 and find stability.
2. Solve differential equation K(70-N) where ko o.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b58230d-93b3-432b-b042-c5aa4698673c%2Fe678723e-ddf7-454d-84cc-23185ecde6b0%2Fekbpde.png&w=3840&q=75)
Transcribed Image Text:1. Find all steady states of differential equationx5x24 and find stability.
2. Solve differential equation K(70-N) where ko o.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Problem 1:
To find all steady states of the given differential equation.
Find all the equilibrium points by setting X\'=0.
![Calculus homework question answer, Step 1, Image 1](https://content.bartleby.com/qna-images/answer/6b58230d-93b3-432b-b042-c5aa4698673c/49f22538-89e6-430e-a225-e5ba3c376d1c/ygas946.png)
Step 2
Thus observe that the equilibrium points are X= -2, -1, 1, 2.
Find the derivative of X'.
![Calculus homework question answer, Step 2, Image 1](https://content.bartleby.com/qna-images/answer/6b58230d-93b3-432b-b042-c5aa4698673c/49f22538-89e6-430e-a225-e5ba3c376d1c/1aw5gs.png)
Step 3
Find (dX'/dt) at the equilibrium points.
![Calculus homework question answer, Step 3, Image 1](https://content.bartleby.com/qna-images/answer/6b58230d-93b3-432b-b042-c5aa4698673c/49f22538-89e6-430e-a225-e5ba3c376d1c/ff0av9j.png)
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