dy 2. Given dr = y°(y – 4)(y + 2) (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -3, y(0) = -2, y(0) : 2' , y(0) = 0, y(0) = 2, y(0) = 3, y(0) = 4, y(0) = 6.
dy 2. Given dr = y°(y – 4)(y + 2) (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -3, y(0) = -2, y(0) : 2' , y(0) = 0, y(0) = 2, y(0) = 3, y(0) = 4, y(0) = 6.
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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Question
My question is in the image.
I have completed part A but I am having trouble with part b. when y(0) = -2 , 0 , or 4 How do I draw that on a graph since they are when the equation is zero?
Transcribed Image Text:2. Given
= y?(y – 4)(y + 2)
dx
(a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the
flow on the phase line (away or towards a critical point).
(b) Next to your phase line, sketch the graph of solutions passing through the given points:
у(0) — — 3, у(0) — — 2, у(0).
y(0) = 0,
2'
y(0) = 2, y(0) = 3, y(0) = 4, y(0) = 6.
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