Consider the autonomous differential equation y = (y – 1)?y(y+ 1). (a) Draw a phase line for this differential equation, labeling each equilibrium with its value, and identifying it as a source, sink, or node. (b) On the axes below, provide (rough) sketches for t20 of the solutions of the initial value problems corresponding to each of the cases: y(0) = 1, y(0) = 1/4, y(0) = -1/2. 1.5 0.5 3 -0.50 -1.5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the autonomous differential equation y = (y – 1)2y(y+ 1).
(a) Draw a phase line for this differential equation, labeling each equilibrium with its value,
and identifying it as a source, sink, or node.
(b) On the axes below, provide (rough) sketches for t2 0 of the solutions of the initial value
problems corresponding to each of the cases: y(0) = 1, y(0) = 1/4, y(0) = -1/2.
1.5
0.5
3
-0.50
-1.5
Transcribed Image Text:Consider the autonomous differential equation y = (y – 1)2y(y+ 1). (a) Draw a phase line for this differential equation, labeling each equilibrium with its value, and identifying it as a source, sink, or node. (b) On the axes below, provide (rough) sketches for t2 0 of the solutions of the initial value problems corresponding to each of the cases: y(0) = 1, y(0) = 1/4, y(0) = -1/2. 1.5 0.5 3 -0.50 -1.5
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