4. Below is the direction field for the differential equation dy = f(x, y) dz for some unspecified function f (x, y).
4. Below is the direction field for the differential equation dy = f(x, y) dz for some unspecified function f (x, y).
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:(a) This direction field should look familiar. It comes from a population model
that we studied. What is the name of the model?
(b) Each of the three labeled points represents an initial condition and hence
specifies an initial value problem when coupled with the differential equa-
tion generating the direction field. Approximately what are the initial
conditions for these three initial value problems?
(c) Suppose that the vertical axis represents the population size of a fish
species and the horizontal axis represents time in months. For each of the
three initial conditions (A, B, and C), write a few sentences describing the
population dynamics described by the solution to the corresponding initial
value problem. Your description should take into account the initial con-
dition and should explain how the population changes as time progresses
as it does.
Transcribed Image Text:4. Below is the direction field for the differential equation
dy
= f(x, y)
dr
for some unspecified function f(x, y).
1200
\\\\\\|
\\\\\
1000
///////////////
800
// ////| /////|| /
// /|||| ||||||| /
/| |||||||||||| /
/| ||||| /B$ / //||/
/| || | |
// ||||/|/
// / |||| //||||| /
600
/| | |
400
/| | ||
200
////
100
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