smallest to largest x, then from smallest to largest y.) x' xy - 4y - 5 y = y²x² smaller x-value X (x, y) = -1,-1 Trace T = X Determinant Δ = X Discriminant T² - 44 = Conclusion unstable spiral point. ✓x larger x-value X (x, y) = 5,5 Trace T = X Determinant Δ = X Discriminant T²-4A = Conclusion unstable spiral point ✓

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from
smallest to largest x, then from smallest to largest y.)
x' = xy - 4y - 5
y' = y² = x²
smaller x-value
X
(x, y) =
-1.-1
T =
Trace
Determinant
A =
X
T² - 4A =
Discriminant
Conclusion
unstable spiral point ✓X
larger x-value
X
(x, y) =
5,5
Trace
T =
X
Determinant
Δ =
X
Discriminant
T²-4A =
Conclusion
unstable spiral point
Transcribed Image Text:Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 4y - 5 y' = y² = x² smaller x-value X (x, y) = -1.-1 T = Trace Determinant A = X T² - 4A = Discriminant Conclusion unstable spiral point ✓X larger x-value X (x, y) = 5,5 Trace T = X Determinant Δ = X Discriminant T²-4A = Conclusion unstable spiral point
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,