Can you please help with differential equations problem attached below? Find the general solution of-21Draw the phase plane showing some trajectories.Discuss the type and stability of the critical point (0,0).

Given that x'=-211-2x The take A=-211-2 Now let's find the eigen values,…

Answered: Find the general solution of (구) -2 1…

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Find the general solution of (구) -2 1 %3D -2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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Can you please help with differential equations problem attached below?

Find the general solution of
-2
1
Draw the phase plane showing some trajectories.
Discuss the type and stability of the critical point (0,0).

Expert Solution

Step 1

Given that $x' = (\begin{matrix} - 2 & 1 \\ 1 & - 2 \end{matrix}) x$

The take $A = (\begin{matrix} - 2 & 1 \\ 1 & - 2 \end{matrix})$

Now let's find the eigen values,

$|A - λ I| = 0 |\begin{matrix} - 2 - λ & 1 \\ 1 & - 2 - λ \end{matrix}| = 0 {(2 + λ)}^{2} - 1 = 0 {(2 + λ)}^{2} = 1 2 + λ = \pm 1 λ = - 3, - 1$

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