(a) Explanation Given: The given differential equation is d x d t = r − k x . Calculation: Consider the given differential equation. d x d t = r − k x (1) Here, r and k are positive constants. Find equilibrium solution of the differential equation. d x d t = 0 r − k x = 0 k x = r x (b) To determine The solution of the differential equation and sketch the graph of x ( t ) .

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Question

Chapter 2.7, Problem 43E

(a)

To determine

The limiting value of x(t) as t→∞.

(b)

To determine

The solution of the differential equation and sketch the graph of x(t).

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Chapter 2.7, Problem 42E

Chapter 2.7, Problem 44E

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The limiting value of x ( t ) as t → ∞ .

Solution Summary: The author explains the limiting value of x(t) and the time at which the concentration is one half of the limit.