Classify (if possible) each critical point of the given second-order differential equation as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Assume y = x'. Order your answers from smallest to largest x, then from smallest to largest y.) x" + x = = (1/12 - 9(ײ) ²)x¹ - x² X (x, y) = (x, y) = Conclusion saddle point unstable spiral point

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Classify (if possible) each critical point of the given second-order differential equation as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Assume y = x'. Order
your answers from smallest to largest x, then from smallest to largest y.)
x² + x − ( ² - 96x²3²) x² -
X" =
x²
2
X
Conclusion
(x, y) =
saddle point
(x, y) =
unstable spiral point
Transcribed Image Text:Classify (if possible) each critical point of the given second-order differential equation as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Assume y = x'. Order your answers from smallest to largest x, then from smallest to largest y.) x² + x − ( ² - 96x²3²) x² - X" = x² 2 X Conclusion (x, y) = saddle point (x, y) = unstable spiral point
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