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(1) Classify the equilibrium solutions of the initial-value problem y'=ay-By², y(0) = yo where a and 3 are small positive numbers. Show that the solution o(r) satisfy lim p(x) = 81X a/B 0 for yo > 0 for yo = 0. For yo<0, o is unbounded as r approaches a certain value depending on yo. Discuss and sketch some particular solutions.

(1) Classify the equilibrium solutions of the initial-value problem y'=ay-By², y(0) = yo where a and 3 are small positive numbers. Show that the solution o(r) satisfy lim p(x) = 81X a/B 0 for yo > 0 for yo = 0. For yo<0, o is unbounded as r approaches a certain value depending on yo. Discuss and sketch some particular solutions.

Advanced Engineering Mathematics
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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(1) Classify the equilibrium solutions of the initial-value problem y' = ay-By², y(0) = yo where a and 3 are small positive numbers. Show that the solution (r) satisfy for yo> 0 for yo = 0. lim p(x) = HIX a/8 0 For yo0, is unbounded as x approaches a certain value depending on yo- Discuss and sketch some particular solutions.
Transcribed Image Text:(1) Classify the equilibrium solutions of the initial-value problem y' = ay-By², y(0) = yo where a and 3 are small positive numbers. Show that the solution (r) satisfy for yo> 0 for yo = 0. lim p(x) = HIX a/8 0 For yo0, is unbounded as x approaches a certain value depending on yo- Discuss and sketch some particular solutions.
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