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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as →. If this behavior depends on the initial value of y at = 0, describe this dependency. y = y(x-4)² Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y() as depends on initial value y() y(4) > 4:y(1) diverges from y = 4. 0 4:y(1) diverges from y = 4. 0

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as →. If this behavior depends on the initial value of y at = 0, describe this dependency. y = y(x-4)² Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y() as depends on initial value y() y(4) > 4:y(1) diverges from y = 4. 0 4:y(1) diverges from y = 4. 0

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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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as →. If this behavior depends on the initial value of y at = 0, describe this dependency. y = y(x-4)² Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y() as depends on initial value y() y(4) > 4:y(1) diverges from y = 4. 0<y()<4:y(1)→ 4. (A) < 0:y(r) diverges from y = 0. Where a = 4. Equilibrium solution: y(0) = 4 Behavior of y() as is independent of initial value y() y()→→ 4 for all y(). Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y(1) as →→ ∞o depends on initial value y(): y() > 4:y(1) diverges from y = 4. 0<y()<4:y()→ 0. y(fe) < 0:y(1) diverges from y = 0. Where d = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y(1) as →∞ depends on initial value y(): y(t) > 0:y(1)→4. y() < 0:y(1) diverges from y = 0. O O A
Transcribed Image Text:Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as →. If this behavior depends on the initial value of y at = 0, describe this dependency. y = y(x-4)² Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y() as depends on initial value y() y(4) > 4:y(1) diverges from y = 4. 0<y()<4:y(1)→ 4. (A) < 0:y(r) diverges from y = 0. Where a = 4. Equilibrium solution: y(0) = 4 Behavior of y() as is independent of initial value y() y()→→ 4 for all y(). Where a = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y(1) as →→ ∞o depends on initial value y(): y() > 4:y(1) diverges from y = 4. 0<y()<4:y()→ 0. y(fe) < 0:y(1) diverges from y = 0. Where d = 4. Equilibrium solutions: y(t) = 0 and y(t) = 4 Behavior of y(1) as →∞ depends on initial value y(): y(t) > 0:y(1)→4. y() < 0:y(1) diverges from y = 0. O O A
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