Consider the system of differential equations For this system, the smaller eigenvalue is (-39/10) [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' = Ay is a differential equation, how would the solution curves behave? • All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. dx dt dy dt = -1.4x +0.75y, = 1.66667-3.4y. and the larger eigenvalue is (-9/10)
Consider the system of differential equations For this system, the smaller eigenvalue is (-39/10) [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' = Ay is a differential equation, how would the solution curves behave? • All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. dx dt dy dt = -1.4x +0.75y, = 1.66667-3.4y. and the larger eigenvalue is (-9/10)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the system of differential equations
For this system, the smaller eigenvalue is (-39/10)
[Note-- you may want to view a phase plane plot (right click to open in a new window).]
If y'= Ay is a differential equation, how would the solution curves behave?
• All of the solutions curves would converge towards 0. (Stable node)
All of the solution curves would run away from 0. (Unstable node)
and the larger eigenvalue is
The solution curves would race towards zero and then veer away towards infinity. (Saddle)
The solution curves converge to different points.
The solution to the above differential equation with initial values (0) = 4, y(0) = 3 is
(t)=
(49/12)*e^((-9/10)*t)-(1/12)*e^((-19/10)*t)
y(t) = (49/12)*e^((-9/10)*t)+(5/12)*e^((-19/10)*t)
da
dt
dy
dt
= -1.4x +0.75y,
= 1.66667 3.4y.
(-9/10)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F649e3b5f-d82f-4a82-a788-6a6fb382daac%2Fce674338-71a5-418a-bfa2-8cee1a657907%2Fhlstc7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
For this system, the smaller eigenvalue is (-39/10)
[Note-- you may want to view a phase plane plot (right click to open in a new window).]
If y'= Ay is a differential equation, how would the solution curves behave?
• All of the solutions curves would converge towards 0. (Stable node)
All of the solution curves would run away from 0. (Unstable node)
and the larger eigenvalue is
The solution curves would race towards zero and then veer away towards infinity. (Saddle)
The solution curves converge to different points.
The solution to the above differential equation with initial values (0) = 4, y(0) = 3 is
(t)=
(49/12)*e^((-9/10)*t)-(1/12)*e^((-19/10)*t)
y(t) = (49/12)*e^((-9/10)*t)+(5/12)*e^((-19/10)*t)
da
dt
dy
dt
= -1.4x +0.75y,
= 1.66667 3.4y.
(-9/10)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
