Question

Find all equilibrium points of the following equations and determine their stabilities (stable, or unstable) a) dx/dt = - x b) dx/dt = x-x^3 c) dx/dt = -x + x^3 d) dx/dt = x- y dy/dt = -y

Name: find all equilibrium points of the following equations and determine their stabilities stable or unstable a dxdt x b dxdt x x3 c dxdt x x3 d dxdt x y dydt y
Uploaded: 2022-04-27T02:53:39-08:00
Duration: 3 min 20 s
Channel: Liliane Martins
Description: find all equilibrium points of the following equations and determine their stabilities stable or unstable a dxdt x b dxdt x x3 c dxdt x x3 d dxdt x y dydt y

          Find all equilibrium points of the following equations and determine their stabilities (stable, or unstable)

a) dx/dt = - x
 
b)  dx/dt = x-x^3
 
c) dx/dt = -x + x^3
 
d) dx/dt = x- y
     dy/dt = -y

Added by Shreyas K.

Calculus with Applications

Margaret L. Lial • Raymond N. Greenwell… 11th Edition

Chapter 10

Instant Answer

Solved by Expert Liliane Martins

04/27/2022

Step 1

a) \( \frac{dx}{dt} = -x \) Set \( -x = 0 \): \[ x = 0 \] b) \( \frac{dx}{dt} = x - x^3 \) Set \( x - x^3 = 0 \): \[ x(1 - x^2) = 0 \] \[ x = 0 \quad \text{or} \quad x^2 = 1 \] \[ x = 0, \quad x = 1, \quad x = -1 \] c) \( \frac{dx}{dt} = -x + x^3 \) Set \( -x + Show more…

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Find all equilibrium points of the following equations and determine their stabilities (stable, or unstable) a) dx/dt = - x b) dx/dt = x-x^3 c) dx/dt = -x + x^3 d) dx/dt = x- y dy/dt = -y