dy dx (a) Sketch the phase line for y, noting that y can be negative for this question. State the equilibrium solutions, and classify each as stable, unstable, or semi-stable. What will happen as x→ ∞ to solutions that have the following initial values: (b) (c) (i) y(0) = -2? (ii) y(0) 0.3 ? (iii) y(1) = 2 ? Consider the autonomous DE given by = · ƒ(y) = y(y − 1)²(y + 1). =
dy dx (a) Sketch the phase line for y, noting that y can be negative for this question. State the equilibrium solutions, and classify each as stable, unstable, or semi-stable. What will happen as x→ ∞ to solutions that have the following initial values: (b) (c) (i) y(0) = -2? (ii) y(0) 0.3 ? (iii) y(1) = 2 ? Consider the autonomous DE given by = · ƒ(y) = y(y − 1)²(y + 1). =
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
Transcribed Image Text:dy
dx
(a) Sketch the phase line for y, noting that y can be negative for this question.
State the equilibrium solutions, and classify each as stable, unstable, or semi-stable.
What will happen as x→ ∞ to solutions that have the following initial values:
(b)
(c)
(i) y(0) = -2?
(ii) y(0) 0.3 ?
(iii) y(1) = 2 ?
Consider the autonomous DE given by
=
=
· ƒ(y) = y(y − 1)²(y + 1).
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