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28. Consider the autonomous equation dy/dt ferentiable, and suppose we know that f(-1) = f(2)= 0. = f(y) where f(y) is continuously dif- (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.

28. Consider the autonomous equation dy/dt ferentiable, and suppose we know that f(-1) = f(2)= 0. = f(y) where f(y) is continuously dif- (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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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: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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