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
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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
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