Explanation Procedure used: From the assumption the first-order linear differential equation formed: w x d y d t = k Where, the plow clears snow at a constant rate of k cubic miles per hours, the time is t in hours and w is the width of plow. In the above expansion neglect the higher term for a solution of series, Calculation: Consider the linear first-order differential equation w x d y d t = k , Let t ∘ be the number of hours before noon when it started snowing and s be the constant rate in miles per hour at which x increases, then for t > − t ∘ , x = s ( t + t ∘ ) , the differential equation becomes, d y d t = k w x 1 ( t + t ∘ ) Integrate the differential equation, ∫ d y d t = ∫ k w x 1 ( t + t ∘ ) y = k w x [ ln ( t + t ∘ ) + c ] When, t = 0 , y = 0 , c = − ln t ∘ Since, c = − ln t ∘ , y = k w x

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

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Chapter 1.3, Problem 37E

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The time it started snowing.

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Chapter 1.3, Problem 36E

Chapter 1.3, Problem 38E

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The time it started snowing.

Solution Summary: The author explains how the plow clears snow at a constant rate of k cubic miles per hour.

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