In Exercises 22-27, describe the long-term behavior of the solution to the differential equation with the given initial condition. 22. y(0)=-1 25. y(0) = -4 dyy²-4y +2 dt 23. y(0) = 2 26. y(0) = 4 24. y(0)=-2 27. y(3)=1
In Exercises 22-27, describe the long-term behavior of the solution to the differential equation with the given initial condition. 22. y(0)=-1 25. y(0) = -4 dyy²-4y +2 dt 23. y(0) = 2 26. y(0) = 4 24. y(0)=-2 27. y(3)=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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HELP ASAP!!!! 25 & 26
Transcribed Image Text:In Exercises 22-27, describe the long-term behavior of the solution to the differential
equation
with the given initial condition.
22. y(0) = -1
25. y(0) = -4
dy
dx = y² = 4y +2
23. y(0) = 2
26. y(0) = 4
24. y(0) = -2
27. y(3) = 1
28. Consider the autonomous equation dy/dt = f(y) where f(y) is continuously dif-
ferentiable, and suppose we know that f(-1) = f(2)= 0.
(a) Describe all the possible behaviors of the solution y(t) that satisfies the initial
condition y(0) = 1.
(b) Suppose also that f(y) > 0 for -1 < y < 2. Describe all the possible behav-
iors of the solution y(t) that satisfies the initial condition y(0) = 1.
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