4. A population's growth over time is modeled using the differential equation P'(t) = rP(t)(K – P(t)), where P(t) is the population at time t, and r and K are constants. (a) Show that this differential equation is separable. (b) Show that 1 1 1 P(t)(K – P(t)) KP(t) K(K – P(t))' (c) Use part (b) to find the general solution for this differential equation.
4. A population's growth over time is modeled using the differential equation P'(t) = rP(t)(K – P(t)), where P(t) is the population at time t, and r and K are constants. (a) Show that this differential equation is separable. (b) Show that 1 1 1 P(t)(K – P(t)) KP(t) K(K – P(t))' (c) Use part (b) to find the general solution for this differential equation.
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. A population's growth over time is modeled using the differential equation
P'() — гP(t)(К — P()),
where P(t) is the population at time t, and r and K are constants.
(a) Show that this differential equation is separable.
(b) Show that
1
1
1
Р()(К — Р())
KP(t)
К (К — Р()*
(c) Use part (b) to find the general solution for this differential equation.
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