Linearization of an equation around fixed points

Click For Summary

Homework Help Overview

The discussion revolves around finding the linearization of the differential equation y' = y(-1+4y-3y^2) at its fixed points, which are identified as y = 0, 1/3, and 1.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the identification of fixed points and the meaning of linearization in this context. There is a question regarding the implications of linearization when the derivative at the fixed points is zero.

Discussion Status

The conversation is ongoing, with participants exploring the concept of linearization and questioning the correctness of the identified fixed points. Some guidance on the definition of linearization has been provided, but there is no consensus on the implications of the derivative being zero at the fixed points.

Contextual Notes

Participants are considering the mathematical definitions and implications of linearization, particularly in relation to fixed points and their derivatives. There is an acknowledgment of potential confusion regarding the behavior of the function at these points.

darkspym7
Messages
10
Reaction score
0

Homework Statement


Find the linearization of the equation y' = y(-1+4y-3y^2) about each of the fixed points


The Attempt at a Solution


I think this is correct for finding fixed points:
Set y' = 0 = y(-1+4y+3y^2), so the fixed points are y = 0, 1/3, 1

What exactly does it mean by linearization of the equation around each of the fixed points?
 
Physics news on Phys.org
linearization

the linearization of a function f about a, (linearization at x=a) is
L(x)= f(a)+f'(a)(x-a) Its pretty much like a taylor series approximation.
 
example

find the linearization of f(x)=x^2 about x=3

L(x)=f(3)+f'(3)(x-3)
L(x)=9+6(x-3)=6x-9
 
But using those fixed points, f'(a) would always be 0. Are those the correct fixed points?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 25 ·
Replies
25
Views
2K
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 27 ·
Replies
27
Views
2K