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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 t = 0, describe this dependency. y = - 2 + 1 -y

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 t = 0, describe this dependency. y = - 2 + 1 -y

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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Question

Differential equations

 

O 0 t t The behavior of y(t) is independent of initial value y(to): y(t) → 1-3 for all y(to). The behavior of y(1) is independent of initial value y(to): y(t)→ 0 for all y(to).
Transcribed Image Text:O 0 t t The behavior of y(t) is independent of initial value y(to): y(t) → 1-3 for all y(to). The behavior of y(1) is independent of initial value y(to): y(t)→ 0 for all y(to).
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 t = 0, describe this dependency. Note that the right sides of these equations depend on / as well as y. 0 Domo y = −2+1-y t The behavior of y() is independent of initial value y(to): y(t)0 for all y(to). Depending on the initial value y(0) either y(1) diverges from in(1 + 7/) − 1 - y = or - y(t) = – sin(1 + 7) – 1.
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 t = 0, describe this dependency. Note that the right sides of these equations depend on / as well as y. 0 Domo y = −2+1-y t The behavior of y() is independent of initial value y(to): y(t)0 for all y(to). Depending on the initial value y(0) either y(1) diverges from in(1 + 7/) − 1 - y = or - y(t) = – sin(1 + 7) – 1.
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