4. Symbiotic Relationship: When two species, such as the rhinoceros and birds, coexist in a symbiotic (dependent) relationship, they either increase together or decrease together. Typical equations for the growth rates of two such species might be da dt dra dt 421+4212₂ =-3x2+2x12. (a) Find an equation relating z₁ and ₂ if #₁ = 5 when z₂ = 1. Meaning, write and use the separation of variables to solve the differential equation. day (b) Find the equilibrium point. (e) Give a phase plane diagram (keep in mind this is a nonlinear system). (d) Based on part (c), what happens to the populations if both populations are greater than their values at equilibrium? Or, if both populations are less than their values at equilibrium?
4. Symbiotic Relationship: When two species, such as the rhinoceros and birds, coexist in a symbiotic (dependent) relationship, they either increase together or decrease together. Typical equations for the growth rates of two such species might be da dt dra dt 421+4212₂ =-3x2+2x12. (a) Find an equation relating z₁ and ₂ if #₁ = 5 when z₂ = 1. Meaning, write and use the separation of variables to solve the differential equation. day (b) Find the equilibrium point. (e) Give a phase plane diagram (keep in mind this is a nonlinear system). (d) Based on part (c), what happens to the populations if both populations are greater than their values at equilibrium? Or, if both populations are less than their values at equilibrium?
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:4. Symbiotic Relationship: When two species, such as the rhinoceros and birds, coexist in a symbiotic (dependent)
relationship, they either increase together or decrease together. Typical equations for the growth rates of two such
species might be
da
dt
dra
dt
-421 +4212₂
=-3x2+2x122.
dr
day
(a) Find an equation relating z, and ₂ if z₁ = 5 when z₂ = 1. Meaning, write and use the separation of
variables to solve the differential equation.
(b) Find the equilibrium point.
(e) Give a phase plane diagram (keep in mind this is a nonlinear system).
(d) Based on part (e), what happens to the populations if both populations are greater than their values at
equilibrium? Or, if both populations are less than their values at equilibrium?
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