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behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y - 6)? Where a = 6. Equilibrium solutions: y(1) = 0 and y(t) = 6. Behavior of y(t) as t o depends on initial value y(to): y(to) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 0. AASVA y(to) < 0: y(t) diverges from y = 0. Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) as t + o depends on initial value y(to): y(to) > 0: y(1) → 6. y(to) < 0: y(t) diverges from y = 0. ASVA Where a - 6. Equilibrium solution: y(t) = 6. Behavior of y(t) as to is independent of initial value y(to): y(to) - 6 for all y(to). Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) as t o depends on initial value y(to): y(10) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 6. y(to) < 0: y(t) diverges from y = 0.

behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y - 6)? Where a = 6. Equilibrium solutions: y(1) = 0 and y(t) = 6. Behavior of y(t) as t o depends on initial value y(to): y(to) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 0. AASVA y(to) < 0: y(t) diverges from y = 0. Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) as t + o depends on initial value y(to): y(to) > 0: y(1) → 6. y(to) < 0: y(t) diverges from y = 0. ASVA Where a - 6. Equilibrium solution: y(t) = 6. Behavior of y(t) as to is independent of initial value y(to): y(to) - 6 for all y(to). Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) as t o depends on initial value y(to): y(10) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 6. y(to) < 0: y(t) diverges from y = 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 t o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y - 6)2 Where a = 6. Equilibrium solutions: y(1) = 0 and y(t) = 6. %3D Behavior of y(t) ast o depends on initial value y(to): y(to) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 0. y(to) < 0: y(1) diverges from y = 0. Where a = 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) ast- o depends on initial value y(to): y(to) > 0: y(t) → 6. y(to) < 0: y(t) diverges from y = 0. Where a - 6. Equilibrium solution: y(1) = 6. ノ Behavior of y(1) as t o is independent of initial value y(to): y(to) - 6 for all y(to). ン Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) 6. Behavior of y(1) as to depends on initial value y(to): y(1o) > 6: y(t) diverges from y = 6. 0 < y(to) < 6: y(t) 6. y(to) < 0: y(1) diverges from y = 0. メイ .....
Transcribed Image Text:Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y - 6)2 Where a = 6. Equilibrium solutions: y(1) = 0 and y(t) = 6. %3D Behavior of y(t) ast o depends on initial value y(to): y(to) > 6: y(1) diverges from y = 6. 0 < y(to) < 6: y(t) 0. y(to) < 0: y(1) diverges from y = 0. Where a = 6. Equilibrium solutions: y(1) = 0 and y(1) = 6. Behavior of y(t) ast- o depends on initial value y(to): y(to) > 0: y(t) → 6. y(to) < 0: y(t) diverges from y = 0. Where a - 6. Equilibrium solution: y(1) = 6. ノ Behavior of y(1) as t o is independent of initial value y(to): y(to) - 6 for all y(to). ン Where a - 6. Equilibrium solutions: y(1) = 0 and y(1) 6. Behavior of y(1) as to depends on initial value y(to): y(1o) > 6: y(t) diverges from y = 6. 0 < y(to) < 6: y(t) 6. y(to) < 0: y(1) diverges from y = 0. メイ .....
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