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st-order differential equation and the initial condition
Chapter 2, Problem 19E(choose chapter or problem)
Consider the autonomous first-order differential equation \(d y / d x=y-y^{3}\) and the initial condition \(y(0)=y_{0}\). By hand, sketch the graph of a typical solution y(x) when \(y_{0}\) has the given values.
(a) \(y_{0}>1\) (b) \(0 < \ y_{0} < 1\)
(c) \(-1 < \ y_{0} < 0\) (d) \(y_{0}<-1\)
Text Transcription:
dy/dx=y-y^3
y(0)=y_0
y_0
y_0>1
0 < y_0 < 1
-1 < y_0 < 0
y_0<-1
Questions & Answers
QUESTION:
Consider the autonomous first-order differential equation \(d y / d x=y-y^{3}\) and the initial condition \(y(0)=y_{0}\). By hand, sketch the graph of a typical solution y(x) when \(y_{0}\) has the given values.
(a) \(y_{0}>1\) (b) \(0 < \ y_{0} < 1\)
(c) \(-1 < \ y_{0} < 0\) (d) \(y_{0}<-1\)
Text Transcription:
dy/dx=y-y^3
y(0)=y_0
y_0
y_0>1
0 < y_0 < 1
-1 < y_0 < 0
y_0<-1
ANSWER:Step 1 of 6
In this problem, we have to draw the graph of a typical solution y(x) when y0 has given values where we consider first order differential equation