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Drawa direction field for the given differential equation. Based on the direction field, deternine the behavior of y as 1 → * If this behavior depends on the initial value of y atr = 0, describe this dependency. Wherea 3. Equilibrium solution: y(1) = 3. Behavior of yir) as t → zis independent of initial value y(to ): y(o) → 3 for all v(n ). Wherea =3.Equilibrium solutians: D. y(1) = 0 and y(t) = 3. Behavior of y(t) as t → »depends on initial value y(1o): y(to) > 3:y(1) diverges from y = 3. 0

Drawa direction field for the given differential equation. Based on the direction field, deternine the behavior of y as 1 → * If this behavior depends on the initial value of y atr = 0, describe this dependency. Wherea 3. Equilibrium solution: y(1) = 3. Behavior of yir) as t → zis independent of initial value y(to ): y(o) → 3 for all v(n ). Wherea =3.Equilibrium solutians: D. y(1) = 0 and y(t) = 3. Behavior of y(t) as t → »depends on initial value y(1o): y(to) > 3:y(1) diverges from y = 3. 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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Wherea=3. Equilibriurn solutions: %3D y(t) = 0 and y(1) = 3. %3D ASSAS SSASS NSASNS 11SA ANNS INIVS 11 Behavior of y(t) as t depends on initial value y(to): y(to) > 3:y(1) diverges fromy 3. %3D NUSN NANA NNI\ NNA 1141 2111 0 < y(tn) < 3: y() 0. NNSSNINS NN11N 411 y(to) < 0:y(r) diverges from y = 0. %3D 7511 1117 D. Wherea-3.Equilibrium solutions: y() = 0 and y(t) = 3. Behavior of y() as t- o depends on initial value y(to): y(to) > 0: y(r) –→ 3. y(to) < 0: y(r) diverges from y = 0. 7111114 t 71
Transcribed Image Text:Wherea=3. Equilibriurn solutions: %3D y(t) = 0 and y(1) = 3. %3D ASSAS SSASS NSASNS 11SA ANNS INIVS 11 Behavior of y(t) as t depends on initial value y(to): y(to) > 3:y(1) diverges fromy 3. %3D NUSN NANA NNI\ NNA 1141 2111 0 < y(tn) < 3: y() 0. NNSSNINS NN11N 411 y(to) < 0:y(r) diverges from y = 0. %3D 7511 1117 D. Wherea-3.Equilibrium solutions: y() = 0 and y(t) = 3. Behavior of y() as t- o depends on initial value y(to): y(to) > 0: y(r) –→ 3. y(to) < 0: y(r) diverges from y = 0. 7111114 t 71
Drawa direction field for the given differential equation. Based on the direction field, deternine the behavior of y as 1 → * If this behavior depends on the initial value of y atr = 0, describe this dependency. y = yv – 3)² Where a 3. Equilibrium solution: (t) = 3. Behavior of yr) as t – is independent of initial value y(to): y(to) → 3 for all véni ). Wherea = 3.Equilibrium solutians: y(t) = 0 and y(1) = 3. Behavior of y(t) as t → »depends on initial value y(fo): y(to) > 3:y(1) diverges from y = 3. 0<y(ro) < 3: y(t)→3. y(to) < 0: y(r) diverges from y = 0.
Transcribed Image Text:Drawa direction field for the given differential equation. Based on the direction field, deternine the behavior of y as 1 → * If this behavior depends on the initial value of y atr = 0, describe this dependency. y = yv – 3)² Where a 3. Equilibrium solution: (t) = 3. Behavior of yr) as t – is independent of initial value y(to): y(to) → 3 for all véni ). Wherea = 3.Equilibrium solutians: y(t) = 0 and y(1) = 3. Behavior of y(t) as t → »depends on initial value y(fo): y(to) > 3:y(1) diverges from y = 3. 0<y(ro) < 3: y(t)→3. y(to) < 0: y(r) diverges from y = 0.
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