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O O 0 0 t t The behavior of y(t) is independent of initial value y(to): y(t) → t - 5 for all y(to). The behavior of y(t) is independent of initial value y(to): y(t) → 0 for all y(to).

O O 0 0 t t The behavior of y(t) is independent of initial value y(to): y(t) → t - 5 for all y(to). The behavior of y(t) is independent of initial value y(to): y(t) → 0 for all y(to).

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 ast → ∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = - 4+1-y Note that the right sides of these equations depend on t as well as y. 0 0 t The behavior of y(t) is independent of initial value y(to): y(t) → 0 for all y(to). Depending on the initial value y(to) either y(t) diverges from 8 n(t + 7) - √2 y = or y(t) = - sint 8 1 sin(t + (+)-1.
Transcribed Image Text:Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast → ∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = - 4+1-y Note that the right sides of these equations depend on t as well as y. 0 0 t The behavior of y(t) is independent of initial value y(to): y(t) → 0 for all y(to). Depending on the initial value y(to) either y(t) diverges from 8 n(t + 7) - √2 y = or y(t) = - sint 8 1 sin(t + (+)-1.
O 0 t t The behavior of y(t) is independent of initial value y(to): y(t) → t - 5 for all y(to). The behavior of y(t) is independent of initial value y(to): y(t) O 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) → t - 5 for all y(to). The behavior of y(t) is independent of initial value y(to): y(t) O for all y(to).
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