Explanation Method used: Separation of variables: “Suppose we are given a first-order separable differential equation in the form, d y d x = f ( x ) g ( y ) Step 1: Separate the variables by writing d y d x = f ( x ) g ( y ) in the form, d y g ( y ) = f ( x ) d x Step 2: Integrate each side of d y g ( y ) = f ( x ) d x with respect to the appropriate variable”. Calculation: The given differential equation is d Q d t = k Q ( C − ln Q ) , where k is a positive constants. Separate the variables in the form of d y g ( y ) = f ( x ) d x . d Q Q ( C − ln Q ) = k d t Integrate the above equation with respect to the appropriate variable as follows. ∫ d Q Q ( C − ln Q ) = k ∫ d t − ∫ d u u = k ∫ d t [ Let u = ( C − ln Q ) d u = − 1 Q d Q ] − ln | u | = k t + P − ln | C − ln Q | = k t + P On further simplification, e − ln | C − ln Q | = e k t + P 1 C − ln Q = P e k t [ ∵ e

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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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 9.3, Problem 25E

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To solve: The differential equation dQdt=kQ(C−lnQ) with the initial condition Q(0)=Q0.

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Chapter 9.3, Problem 23E

Chapter 9.3, Problem 26E

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Applied Calculus for the Managerial, Life, and Social Sciences

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The differential equation d Q d t = k Q ( C − ln Q ) with the initial condition Q ( 0 ) = Q 0 .

Solution Summary: The author explains how to solve a differential equation with the initial condition Q(0)=Q_0.

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To solve: The differential equation dQdt=kQ(C−lnQ) with the initial condition Q(0)=Q0.

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Chapter 9 Solutions