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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as! → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y-2)² O O 276 a a Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞ depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 y(to) < 2: y(t) → 0. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → ∞o is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(to): y(to) > 0: y(t) → 2. y(to) < 0: y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(10): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 2. y(to) < 0: y(t) diverges from y = 0.

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as! → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y-2)² O O 276 a a Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞ depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 y(to) < 2: y(t) → 0. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → ∞o is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(to): y(to) > 0: y(t) → 2. y(to) < 0: y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(10): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 2. 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 ✓ → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y - 2)² O O a a 1 VATNEVINS VARVAVIVA //// " t Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞ depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2: y(t) 0. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → co is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞o depends on initial value y(to): y(to) > 0: y(t) → 2. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞ depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(1)→ 2. y(to) < 0:y(1) diverges from y = 0.
Transcribed Image Text:Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as ✓ → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y - 2)² O O a a 1 VATNEVINS VARVAVIVA //// " t Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞ depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2: y(t) 0. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → co is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞o depends on initial value y(to): y(to) > 0: y(t) → 2. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) ast → ∞ depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(1)→ 2. y(to) < 0:y(1) diverges from y = 0.
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