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Math / Differential Equations and Linear Algebra 3 / Chapter 2.2 / Problem 12P

Differential Equations and Linear Algebra | 3rd Edition | ISBN: 9780136054252 | Authors: C. Henry Edwards, David E. Penney

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In problem first solve the equation f(x) = 0

Chapter 2, Problem 12P

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QUESTION:

In problem first solve the equation f(x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f(x). Then analyze the sign of f(x) to determine whether each critical point is stable or unstable, and construct the comsfx/iuling phase diagram for the differential equation. Next, solve the differential equation explicitly for x(t) in terms of t. Finally, use either the exact solution or a computer-generated slope field to sketch typical solution curves for the given differential equation, and verify visually the stability of each critical point.

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QUESTION:

In problem first solve the equation f(x) = 0 to find the critical points of the given autonomous differential equation dx/dt = f(x). Then analyze the sign of f(x) to determine whether each critical point is stable or unstable, and construct the comsfx/iuling phase diagram for the differential equation. Next, solve the differential equation explicitly for x(t) in terms of t. Finally, use either the exact solution or a computer-generated slope field to sketch typical solution curves for the given differential equation, and verify visually the stability of each critical point.

ANSWER:

SolutionStep 1 of 4In this problem, we need to determine the critical point of the given differential equation, and we have to predict its stability, and we solve the differential equation and also sketch the typical solution curves.

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