Determine all equilibrium solutions and classify as stable, semi-stable, or unstable. dx =(x²-4)² dt x= ±2 Semi-stable, None Stable or Unstable x=2 Semi-Stable, x=-2 Unstable C. x=2 Unstable, d. None Unstable, e. x=2 Unstable, a. b. x = -2 Semi-stable x = ±2 Stable x = -2 Stable

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Determine all equilibrium solutions and classify as stable, semi-stable, or unstable.**

\[\frac{dx}{dt} = (x^2 - 4)^2\]

a. \(x = \pm 2\) Semi-stable, None Stable or Unstable

b. \(x = 2\) Semi-Stable, \(x = -2\) Unstable

c. \(x = 2\) Unstable, \(x = -2\) Semi-stable

d. None Unstable, \(x = \pm 2\) Stable

e. \(x = 2\) Unstable, \(x = -2\) Stable

**Options:**
- a
- b
- c
- d
- e
Transcribed Image Text:**Determine all equilibrium solutions and classify as stable, semi-stable, or unstable.** \[\frac{dx}{dt} = (x^2 - 4)^2\] a. \(x = \pm 2\) Semi-stable, None Stable or Unstable b. \(x = 2\) Semi-Stable, \(x = -2\) Unstable c. \(x = 2\) Unstable, \(x = -2\) Semi-stable d. None Unstable, \(x = \pm 2\) Stable e. \(x = 2\) Unstable, \(x = -2\) Stable **Options:** - a - b - c - d - e
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