Consider the differential equation: dy/dx = y(3 −y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. rey)-(-y) Dety dy dz And y (3-9) Step size 01 Solution A Solution B Input.. Solution C Solution D sca ACEA 2) To what value does y(x) approach, as x → ∞o, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x → ∞o, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other solutions? Why?
Consider the differential equation: dy/dx = y(3 −y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. rey)-(-y) Dety dy dz And y (3-9) Step size 01 Solution A Solution B Input.. Solution C Solution D sca ACEA 2) To what value does y(x) approach, as x → ∞o, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x → ∞o, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other solutions? Why?
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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Transcribed Image Text:Consider the differential equation: dy/dx = y(3 - y)
1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can
drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture
a screenshot showing all the solution curves and insert below.
f'(x)=y(3-y)
Kin/5
-5
Density
Length
dy
de
-8
Step size 0.1
Ymas
y (3-9)
Input.
✔Solution A
Solution B
Solution C
Solution D
DCQ=
AC:
2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does
y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and
answer in terms of what you know about the slope field and its effect on the solution.
-
3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points
A,B,C,D. How is the solution through Point C different from the other solutions? Why?
4) Find the equilibrium solution(s) for this differential equation.
5) Is the behavior of y(x) as x →
co dependent on the initial value? Why or why not?
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