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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
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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HELP ASAP!!!! 25 & 26

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.
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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