(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

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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.