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Assume that 0 < Po < M in equation dP 3D КP(М - Р), Р(0) — Ро. dt (a) Find the equilibrium points and determine their nature. (b) Show that the solution to this equation by the method of separation of variables is MP Po+ (M – Po)e-kMt P(t - (c) Show that P(t) < M for all t2 0. (d) Show that lim,- P(t) = M

Assume that 0 < Po < M in equation dP 3D КP(М - Р), Р(0) — Ро. dt (a) Find the equilibrium points and determine their nature. (b) Show that the solution to this equation by the method of separation of variables is MP Po+ (M – Po)e-kMt P(t - (c) Show that P(t) < M for all t2 0. (d) Show that lim,- P(t) = M

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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Assume that 0 < P, < M in equation dP 3D КP(М — Р), Р(0) — Ро. dt (a) Find the equilibrium points and determine their nature. (b) Show that the solution to this equation by the method of separation of variables is P(t)- MP Po + (M – Po)e-kMt (c) Show that P(t) < M for all t> 0. (d) Show that lim-0 P(t) = M
Transcribed Image Text:Assume that 0 < P, < M in equation dP 3D КP(М — Р), Р(0) — Ро. dt (a) Find the equilibrium points and determine their nature. (b) Show that the solution to this equation by the method of separation of variables is P(t)- MP Po + (M – Po)e-kMt (c) Show that P(t) < M for all t> 0. (d) Show that lim-0 P(t) = M
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