Populations of aphids and ladybugs are modeled by the equations LA 400- -0.5L + 0.0001AL (a) Find the equilibrium solutions and explain their significance. (b) Find an expression for dL/dA. (c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common? 300+ 200 100- dA dt … -- 24 -0.01AL dL dt 5000 TELEZ-NIAL 10000 15000 A (d) Suppose that at time=0 there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change. (e) Use part (d) to make rough sketches of the aphid and ladybug populations as functions of t. How are the graphs related to each other?
Populations of aphids and ladybugs are modeled by the equations LA 400- -0.5L + 0.0001AL (a) Find the equilibrium solutions and explain their significance. (b) Find an expression for dL/dA. (c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common? 300+ 200 100- dA dt … -- 24 -0.01AL dL dt 5000 TELEZ-NIAL 10000 15000 A (d) Suppose that at time=0 there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change. (e) Use part (d) to make rough sketches of the aphid and ladybug populations as functions of t. How are the graphs related to each other?
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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Can you solve the following CALC 2 problem attached?
Transcribed Image Text:Populations of aphids and ladybugs are modeled by the
equations
LA
400-
-0.5L + 0.0001AZ
(a) Find the equilibrium solutions and explain their
significance.
(b) Find an expression for dL/dA.
(c) The direction field for the differential equation in part (b)
is shown. Use it to sketch a phase portrait. What do the
phase trajectories have in common?
300+
200
100-
dA
dt
…
-- 24 -0.01AL
dL
dt
5000
TELEZ-NIAL
10000
15000 A
(d) Suppose that at time t=0 there are 1000 aphids and
200 ladybugs. Draw the corresponding phase trajectory
and use it to describe how both populations change.
(e) Use part (d) to make rough sketches of the aphid and
ladybug populations as functions of t. How are the graphs
related to each other?
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