If you look at the attached picture, I already performed all of the work and determined that x_1 and x_2 converge to 0, all I need help with is describing the results and whether or not they make sense given the problem and it's context. Is this is something you can help me with? Thank you!
If you look at the attached picture, I already performed all of the work and determined that x_1 and x_2 converge to 0, all I need help with is describing the results and whether or not they make sense given the problem and it's context. Is this is something you can help me with? Thank you!
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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If you look at the attached picture, I already performed all of the work and determined that x_1 and x_2 converge to 0, all I need help with is describing the results and whether or not they make sense given the problem and it's context.
Is this is something you can help me with? Thank you!
![Consider the system of differential equations x₁ = 5x₁ + x₂
and x₂ = 4x₁2x2. Use MATLAB to plot the eigenvectors and direction
field of this system on a single plot. Make sure to label both axes and title
your figure. Generate your plots for -1 ≤ x ≤ 1 and -1 ≤ x₂ ≤ 1 and set
both X₁ and ₂ axes to limits of [-1 1].
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1
0.8
0.6
0.4
0.2
0
Consider the same system of differential equations
Use MATLAB to plot the phase portrait of this system of differential
equations. Make sure to label both axes and title your figure. Use the same
x1-axis and x2-axis limits
-02
-0.4
-0.6
-0.8
Problem 1 - Eigenvectorsand direction field
-1
-0.5
-0.5
0
X1
Problem 2-Phase Portrait.
0.5
0.5
Analyze the phase portrait from Problem 2 for the initial
conditions of x₁(0) = 0.5 and x₂(0) = 0.3. As t→ ∞o to what values do
x₁(1) and x₂(1) converge to?
To find the steady state, we set the derivatives in the system of equations to zero and solve for x1
and x2. This gives us the equations -5x1 + x2 = 0 and 4x1 - 2x2 = 0. Solving these equations gives
x1 = 0 and x2 = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68707cfa-83a2-43f4-ad61-0c752e608c06%2F22eec3b9-0ad1-4caa-af4a-c03853d50e56%2Fcmfel7p_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations x₁ = 5x₁ + x₂
and x₂ = 4x₁2x2. Use MATLAB to plot the eigenvectors and direction
field of this system on a single plot. Make sure to label both axes and title
your figure. Generate your plots for -1 ≤ x ≤ 1 and -1 ≤ x₂ ≤ 1 and set
both X₁ and ₂ axes to limits of [-1 1].
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1
0.8
0.6
0.4
0.2
0
Consider the same system of differential equations
Use MATLAB to plot the phase portrait of this system of differential
equations. Make sure to label both axes and title your figure. Use the same
x1-axis and x2-axis limits
-02
-0.4
-0.6
-0.8
Problem 1 - Eigenvectorsand direction field
-1
-0.5
-0.5
0
X1
Problem 2-Phase Portrait.
0.5
0.5
Analyze the phase portrait from Problem 2 for the initial
conditions of x₁(0) = 0.5 and x₂(0) = 0.3. As t→ ∞o to what values do
x₁(1) and x₂(1) converge to?
To find the steady state, we set the derivatives in the system of equations to zero and solve for x1
and x2. This gives us the equations -5x1 + x2 = 0 and 4x1 - 2x2 = 0. Solving these equations gives
x1 = 0 and x2 = 0.
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