For each of the following systems, (2.1) dx = 2 – x dt (2.2) dx = (x – 1) x? dt - (2.3) dx (r – 2) x (x + 1) dt draw a sketch of: (a) dx/dt as a function of x, (b) the phase line, (c) the solution curve x (t) if the system starts at x (0) = 1.

For each of the following systems, (2.1) dx = 2 – x dt (2.2) dx = (x – 1) x? dt - (2.3) dx (r – 2) x (x + 1) dt draw a sketch of: (a) dx/dt as a function of x, (b) the phase line, (c) the solution curve x (t) if the system starts at x (0) = 1.

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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Differential Equations

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Question

For each of the following systems,
(2.1)
dx
= 2 – x
dt
(2.2)
dx
= (x – 1) x²
dt
(2.3)
dx
(r – 2) x (x + 1)
dt
draw a sketch of:
(a) dx/dt as a function of x,
(b) the phase line,
(c) the solution curve x (t) if the system starts at x (0) = 1.

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