dp Consider the differential equation=p(p-1)(2-p) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below. dt (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. A. AF Q If p(0) = 3, then lim p(t)= 2. The population will decrease and level off. 1→ +00 (b) If the initial population is 3000 [that is, p(0) = 3], what can be said about the limiting population lim p(t)? (c) If p(0) = 1.8, what can be said about the limiting population lim p(t)? If p(0) = 1.8, then lim p(t) = 2. The population will increase and level off. 1→ +00 (d) If p(0) = 0.4, what can be said about the limiting population lim p(t)? B If p(0) = 0.4, then lim p(t)=. The population will 1→ +00 AF C Q Q O C. Ap Q

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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solve only d) and options for box are

a) decrease without limit

b) increase without limit

c) increase and level off

d) decrease and level off

dp
Consider the differential equation=p(p-1)(2-p) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below.
(a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below.
B.
Ap
OA.
AP
Q
(b) If the initial population is 3000 [that is, p(0) = 3], what can be said about the limiting population lim p(t)?
t→ +∞o
If p(0) = 3, then lim p(t)= 2. The population will decrease and level off.
t→ +∞o
(c) If p(0) = 1.8, what can be said about the limiting population lim p(t)?
t→ +00
If p(0) = 1.8, then lim p(t) = 2. The population will increase and level off.
(d) If p(0) = 0.4, what can be said about the limiting population lim p(t)?
t→ +∞o
If p(0) = 0.4, then lim p(t)=. The population will
t→ +∞o
IIIII
Q
C
M
O C.
AP
1171717
Q
✔
Transcribed Image Text:dp Consider the differential equation=p(p-1)(2-p) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below. (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. B. Ap OA. AP Q (b) If the initial population is 3000 [that is, p(0) = 3], what can be said about the limiting population lim p(t)? t→ +∞o If p(0) = 3, then lim p(t)= 2. The population will decrease and level off. t→ +∞o (c) If p(0) = 1.8, what can be said about the limiting population lim p(t)? t→ +00 If p(0) = 1.8, then lim p(t) = 2. The population will increase and level off. (d) If p(0) = 0.4, what can be said about the limiting population lim p(t)? t→ +∞o If p(0) = 0.4, then lim p(t)=. The population will t→ +∞o IIIII Q C M O C. AP 1171717 Q ✔
Expert Solution
Step 1

First using the phase portrait, we will find out stability of the fixed points. Then for different initial conditions, we will draw some solution trajectories and phase line.

 

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