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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).
Transcribed Image Text: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'=-211-2x

The take A=-211-2

Now let's find the eigen values,

A-λI=0-2-λ11-2-λ=02+λ2-1=02+λ2=12+λ=±1λ=-3,-1

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