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Consider the model of two competing populations defined by (dx = x(2 – 0.4x – 0.3y) dt |dy - = y(1 – 0.1y – 0.3x) dt Where the populations x(t) and y(t) are measured in thousands.

Consider the model of two competing populations defined by (dx = x(2 – 0.4x – 0.3y) dt |dy - = y(1 – 0.1y – 0.3x) dt Where the populations x(t) and y(t) are measured in thousands.

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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Consider the model of two competing populations defined by (dx = x(2 – 0.4x – 0.3y) dt dy %3D у (1 - 0.1у- 0.Зx) dt Where the populations x(t) and y(t) are measured in thousands. a) Solve the system of differential equations assuming x(0) = 2 and y(0) = 7. b) Estimate the populations at t = 10. c) Graph the solutions in a single figure and make the corresponding comparisons.
Transcribed Image Text:Consider the model of two competing populations defined by (dx = x(2 – 0.4x – 0.3y) dt dy %3D у (1 - 0.1у- 0.Зx) dt Where the populations x(t) and y(t) are measured in thousands. a) Solve the system of differential equations assuming x(0) = 2 and y(0) = 7. b) Estimate the populations at t = 10. c) Graph the solutions in a single figure and make the corresponding comparisons.
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