Program Explanation Given information: The differential equation is d y d x = ( x − 2 ) 2 and initial condition is y ( 2 ) = 1 . Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables as, ∫ d y g ( y ) = ∫ f ( x ) d x The integral of the function x n can be calculated as, ∫ x n d x = x n + 1 n + 1 + c Here, c is called the constant of integration. Calculation: The given differential equation is d y d x = ( x − 2 ) 2 . Separate the variables of the above differential equation as, d y = ( x − 2 ) 2 d x Now integrate the equation on both the sides. ∫ d y = ∫ ( x − 2 ) 2 d x Now evaluate the above integral as, y = ( x − 2 ) 3 3 + C

5th Edition

ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

Question

Chapter 1.2, Problem 2P

Program Plan Intro

To find: A particular function y=f(x) that satisfy the differential equation dydx=(x−2)2 and the initial condition y(2)=1 .

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Chapter 1.2, Problem 1P

Chapter 1.2, Problem 3P

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Chapter 1 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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A particular function y = f ( x ) that satisfy the differential equation d y d x = ( x − 2 ) 2 and the initial condition y ( 2 ) = 1 .

Solution Summary: The author explains how the differential equation dy-dx=(x-2)2 can be calculated with the help of separating the variables.

Concept explainers

To find: A particular function y=f(x) that satisfy the differential equation dydx=(x−2)2 and the initial condition y(2)=1 .

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Chapter 1 Solutions