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(a) Suppose a = b = 1 in the Gompertz differential equation, = P(a - b In(P)) (see (7) in Section 3.2). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases Po > e and 0 < P, e-1 and 0 < P, < e.

(a) Suppose a = b = 1 in the Gompertz differential equation, = P(a - b In(P)) (see (7) in Section 3.2). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases Po > e and 0 < P, e-1 and 0 < P, < e.

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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(a) Suppose a = b = 1 in the Gompertz differential equation, = P(a - b In(P)) (see (7) in Section 3.2). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases Po > e and 0 < P, < e. P P P. (b) Suppose a = 1, b = -1 in the Gompertz differential equation. Use a nevw phase portrait to sketch representative solution curves corresponding to the cases P, > e-1 and 0 < P. <e.
Transcribed Image Text:(a) Suppose a = b = 1 in the Gompertz differential equation, = P(a - b In(P)) (see (7) in Section 3.2). Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases Po > e and 0 < P, < e. P P P. (b) Suppose a = 1, b = -1 in the Gompertz differential equation. Use a nevw phase portrait to sketch representative solution curves corresponding to the cases P, > e-1 and 0 < P. <e.
(b) Suppose a = 1, b = -1 in the Gompertz differential equation. Use a new phase portrait to sketch representative solution curves corresponding to the cases P,> e-1 and 0 < P, ce. 1/e 1/e 1/e 1/e (c) Find an explicit solution of the Gompertz differential equation subject to P(0) = Po: P(t) =
Transcribed Image Text:(b) Suppose a = 1, b = -1 in the Gompertz differential equation. Use a new phase portrait to sketch representative solution curves corresponding to the cases P,> e-1 and 0 < P, ce. 1/e 1/e 1/e 1/e (c) Find an explicit solution of the Gompertz differential equation subject to P(0) = Po: P(t) =
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