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P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.

P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.

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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P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.
Transcribed Image Text:P5, 40pts. Revisiting logistic growth. This problem considers the case where the logistic equation has a slowly varying carrying capacity k(et), where k is a smooth, positive function, but otherwise arbitrary. The equation is 3-(1-844)) y = ry k(et) where y(0) = a and r, a are positive constants. Obtain a first-term approximation of the solution valid for large t. For +10, attempt to determine the second term in the approximation.
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