Explanation The function is, y = 100 1 + 99 e − 5 t . Differentiate y with respect to t , d y d t = d d t ( 100 1 + 99 e − 5 t ) = 100 d d t ( 1 + 99 e − 5 t ) − 1 = − 100 ( 1 + 99 e − 5 t ) − 2 d d t ( 99 e − 5 t ) = − 100 ( 1 + 99 e − 5 t ) − 2 ( 99 ( − 5 e − 5 t ) ) Simplify further as follows, d y d t = − 100 ( 1 + 99 e − 5 t ) − 2 ( − 495 e − 5 t ) = 49 , 500 e − 5 t ( 1 + 99 e − 5 t ) 2 Substitute d y d t = 49 , 500 e − 5 t ( 1 + 99 e − 5 t ) 2 in d y d t = 5 ( 1 − y 100 ) y to check whether the function satisfies the differential equation or not. 49 , 500 e − 5 t ( 1 + 99 e − 5 t ) 2 = 5 ( 1 − y 100 ) ( 100 1 + 99 e − 5 t )

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ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 16, Problem 13RE

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Whether the given statement, “The function y=1001+99e−5t satisfies the differential equation dydt=5(1−y100)y ” is true or false.

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Chapter 16, Problem 12RE

Chapter 16, Problem 14RE

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Whether the given statement, “The function y = 100 1 + 99 e − 5 t satisfies the differential equation d y d t = 5 ( 1 − y 100 ) y ” is true or false.

Solution Summary: The author explains that the function y=1001+99e-5t satisfies the differential equation.

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Whether the given statement, “The function y=1001+99e−5t satisfies the differential equation dydt=5(1−y100)y ” is true or false.

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Chapter 16 Solutions