Explanation Given information: The differential equation is y ' = − k ( y − b ) . Formula used : ∫ d x ( x ± a ) = log ( x ± a ) + C Calculation: y ' = − k ( y − b ) . (Given) ⇒ d y d t = − k ( y − b ) ⇒ d y ( y − b ) = − k d t Integrating both sides, we get ∫ d y ( y − b ) = − k ∫ d t ⇒ log ( y − b ) = − k t + k ⇒ y − b = e − k t + c ⇒ y = e c . e − k t + b ⇒ y = b + e c

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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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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Chapter 10.2, Problem 3PQ

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True or False:If k>0, then all solutions of y'=−k(y−b) approach the same limit as t→∞ .

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Chapter 10.2, Problem 2PQ

Chapter 10.2, Problem 4PQ

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True or False: If k > 0 , then all solutions of y ' = − k ( y − b ) approach the same limit as t → ∞ .

Solution Summary: The author explains that all solutions of y'=-k(y-b) approach the same limit.

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True or False:If k>0, then all solutions of y'=−k(y−b) approach the same limit as t→∞ .

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Chapter 10 Solutions

True or False: If k &gt; 0 , then all solutions of y ' = − k ( y − b ) approach the same limit as t → ∞ .

Solution Summary: The author explains that all solutions of y'=-k(y-b) approach the same limit.

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True or False:If k>0, then all solutions of y'=−k(y−b) approach the same limit as t→∞ .

Want to see the full answer?

Chapter 10 Solutions

True or False: If k > 0 , then all solutions of y ' = − k ( y − b ) approach the same limit as t → ∞ .