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Use the substitution u N-1/2 to show that the exact solution of the equation (1) satisfying the initial condition N(0) No > 0 is given by N(t) = [K-/2 + (N,V2 – K-1/2 Determine the behaviour of the solution in the limit of t o.

Use the substitution u N-1/2 to show that the exact solution of the equation (1) satisfying the initial condition N(0) No > 0 is given by N(t) = [K-/2 + (N,V2 – K-1/2 Determine the behaviour of the solution in the limit of t o.

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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The dynamics of a fish population is described by the Richard's growth law dN N rN (1) dt K where N = N(t) is the population size depending on the continuous time variable t, and r and K are positive constants.
Transcribed Image Text:The dynamics of a fish population is described by the Richard's growth law dN N rN (1) dt K where N = N(t) is the population size depending on the continuous time variable t, and r and K are positive constants.
(iii) Use the substitution u = N-/2 to show that the exact solution of the equation (1) satisfying the initial condition N(0) = No > 0 is given by N(t) = [K-2. -1/2) Determine the behaviour of the solution in the limit of t oo.
Transcribed Image Text:(iii) Use the substitution u = N-/2 to show that the exact solution of the equation (1) satisfying the initial condition N(0) = No > 0 is given by N(t) = [K-2. -1/2) Determine the behaviour of the solution in the limit of t oo.
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