Explanation Given: The mixing problem model is, d x d t = a − b x ; a , b > 0 Approach: The equilibrium solution is given by calculating d x d t = 0 . Calculation: The mixing model is given as, d x d t = a − b x ... ( 1 ) Solve the equation ( 1 ) as, ∫ d x ( a − b x ) = ∫ d t ... ( 2 ) Put a − b x = m Differentiate a − b x = m − b d x = d m d x = − d m b Substitute the value of d x in equation ( 2 ) − 1 b ∫ d m m = ∫ d t − 1 b ∫ d m m = ∫ d t − 1 b ln ( m ) = t + C

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 3.2, Problem 10E

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Any solution to the given mixing problem approaches equilibrium solution x(t)≡a/b as t approaches +∞.

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Chapter 3.2, Problem 9E

Chapter 3.2, Problem 11E

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Fundamentals of Differential Equations and Boundary Value Problems

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Any solution to the given mixing problem approaches equilibrium solution x ( t ) ≡ a / b as t approaches + ∞ .

Solution Summary: The author explains that any solution to the given mixing problem approaches equilibrium solution x(t)equiv a/b as +infty

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Any solution to the given mixing problem approaches equilibrium solution x(t)≡a/b as t approaches +∞.

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Any solution to the given mixing problem approaches equilibrium solution x ( t ) ≡ a / b as t approaches + ∞ .

Solution Summary: The author explains that any solution to the given mixing problem approaches equilibrium solution x(t)equiv a/b as +infty

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To show: Any solution to the given mixing problem approaches equilibrium solution x(t)≡a/b as t approaches +∞.

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Chapter 3 Solutions

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Any solution to the given mixing problem approaches equilibrium solution x(t)≡a/b as t approaches +∞.