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dy 2. You are told that the autonomous differential equation = f(y) (with continuously dt differentiable right-hand side f(y)) has a sink at y = -2, a node at y = 0, another node at y = 2, and no other equilibrium points. a) Sketch the graph of a possible function f(y) with this property. b) Sketch the phase line. c) In a t-y coordinate system, sketch the two solutions y(t) with y(0) = -1 and y(0) = 1.

dy 2. You are told that the autonomous differential equation = f(y) (with continuously dt differentiable right-hand side f(y)) has a sink at y = -2, a node at y = 0, another node at y = 2, and no other equilibrium points. a) Sketch the graph of a possible function f(y) with this property. b) Sketch the phase line. c) In a t-y coordinate system, sketch the two solutions y(t) with y(0) = -1 and 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
Problem 1RQ
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dy 2. You are told that the autonomous differential equation = f(y) (with continuously dt differentiable right-hand side f(y)) has a sink at y = -2, a node at y = 0, another node at y = 2, and no other equilibrium points. a) Sketch the graph of a possible function f(y) with this property. b) Sketch the phase line. c) In a t-y coordinate system, sketch the two solutions y(t) with y(0) = -1 and y(0) = 1.
Transcribed Image Text:dy 2. You are told that the autonomous differential equation = f(y) (with continuously dt differentiable right-hand side f(y)) has a sink at y = -2, a node at y = 0, another node at y = 2, and no other equilibrium points. a) Sketch the graph of a possible function f(y) with this property. b) Sketch the phase line. c) In a t-y coordinate system, sketch the two solutions y(t) with y(0) = -1 and y(0) = 1.
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