1. Consider the differential equation dy = y(y + 1)²(2 – y) dt a. Sketch the vs. y graph. b. Draw a sketch indicating the long-term behaviors of all the qualitatively different solutions, including (in a different color, or bold) the solution with the initial condition y(0) = 1.
1. Consider the differential equation dy = y(y + 1)²(2 – y) dt a. Sketch the vs. y graph. b. Draw a sketch indicating the long-term behaviors of all the qualitatively different solutions, including (in a different color, or bold) the solution with the initial condition y(0) = 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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I only need 1-b. Please write process(explanation) and don't use the calculator. I will attach the answer and question.
1. Consider the differential equation
??
?? = ?(? + 1)
2
(2 − ?)
a. Sketch the ??
??
vs. y graph.
b. Draw a sketch indicating the long-term behaviors of all the qualitatively different solutions,
including (in a different color, or bold) the solution with the initial condition ?(0) = 1.
Transcribed Image Text:1. Consider the differential equation
dy
ay = yy + 1)²(2 – y)
dt
dy
a. Sketch the vs. y graph.
dt
b. Draw a sketch indicating the long-term behaviors of all the qualitatively different solutions,
including (in a different color, or bold) the solution with the initial condition y(0) = 1.
Transcribed Image Text:b. Draw a sketch indicating the long-term behaviors of all the qualitatively different solutions,
including (in a different color, or bold) the solution with the initial condition y(0) = 1.
台
dy
>0
台。
大
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