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Problem 2: A symbiotic (close + long-term) relationship between two species is said to be: Mutualistic if the relationship benefits both species Commensal if the relationship benefits one species while the other is unaffected Parasitic if the relationship benefits one species while the other is harmed ● Let a, b, c, and d be positive constants. Let x(t) and y(t) represent the population size of two different species. Note that the product xy is a representation of the amount of interaction between the two species. a) In the differential equation - = ax + bxy, is the species represented by x(t) benefited, dt harmed, or unaffected when the two species interact? dy dt b) In the differential equation = cy, is the species represented by y(t) benefited, harmed, or unaffected when the two species interact? c) If the population size of the two species was represented by the system of differential equations, : dx dt dy dt = ax + bxy = cy What is the relationship between the two species: mutualistic, commensal, or parasitic?

Problem 2: A symbiotic (close + long-term) relationship between two species is said to be: Mutualistic if the relationship benefits both species Commensal if the relationship benefits one species while the other is unaffected Parasitic if the relationship benefits one species while the other is harmed ● Let a, b, c, and d be positive constants. Let x(t) and y(t) represent the population size of two different species. Note that the product xy is a representation of the amount of interaction between the two species. a) In the differential equation - = ax + bxy, is the species represented by x(t) benefited, dt harmed, or unaffected when the two species interact? dy dt b) In the differential equation = cy, is the species represented by y(t) benefited, harmed, or unaffected when the two species interact? c) If the population size of the two species was represented by the system of differential equations, : dx dt dy dt = ax + bxy = cy What is the relationship between the two species: mutualistic, commensal, or parasitic?

Advanced Engineering Mathematics
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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Problem 2: A symbiotic (close + long-term) relationship between two species is said to be: Mutualistic if the relationship benefits both species Commensal if the relationship benefits one species while the other is unaffected Parasitic if the relationship benefits one species while the other is harmed ● Let a, b, c, and d be positive constants. Let x(t) and y(t) represent the population size of two different species. Note that the product xy is a representation of the amount of interaction between the two species. dx dt a) In the differential equation = ax + bxy, is the species represented by x(t) benefited, harmed, or unaffected when the two species interact? dy dt b) In the differential equation = cy, is the species represented by y(t) benefited, harmed, or unaffected when the two species interact? c) If the population size of the two species was represented by the system of differential equations, : dx dt = ax + bxy dy dt What is the relationship between the two species: mutualistic, commensal, or parasitic? = cy d) Write down a system of differential equations that might represent two species with a mutualistic relationship.
Transcribed Image Text:Problem 2: A symbiotic (close + long-term) relationship between two species is said to be: Mutualistic if the relationship benefits both species Commensal if the relationship benefits one species while the other is unaffected Parasitic if the relationship benefits one species while the other is harmed ● Let a, b, c, and d be positive constants. Let x(t) and y(t) represent the population size of two different species. Note that the product xy is a representation of the amount of interaction between the two species. dx dt a) In the differential equation = ax + bxy, is the species represented by x(t) benefited, harmed, or unaffected when the two species interact? dy dt b) In the differential equation = cy, is the species represented by y(t) benefited, harmed, or unaffected when the two species interact? c) If the population size of the two species was represented by the system of differential equations, : dx dt = ax + bxy dy dt What is the relationship between the two species: mutualistic, commensal, or parasitic? = cy d) Write down a system of differential equations that might represent two species with a mutualistic relationship.
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