Program Explanation Given information: The differential equation is d y d x = x e − x and initial condition is y ( 0 ) = 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 integration of the function f ( x ) g ( x ) can be evaluated by parts as, ∫ f ( x ) g ( x ) = f ( x ) ∫ g ( x ) d x − ∫ ( d d x ( f ( x ) ) ∫ g ( x ) d x ) d x Here, f ( x ) is the first function and g ( x ) is the second function. The integration of the function of e − x is − e − x . Calculation: The given differential equation is d y d x = x e − x . Separate the variables of the above differential equation as, d y = x e − x d x Now integrate the equation on both the sides

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 1.2, Problem 10P

Program Plan Intro

To find: A particular function y=f(x) that satisfy the differential equation dydx=xe−x and the initial condition is y(0)=1 .

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Chapter 1.2, Problem 9P

Chapter 1.2, Problem 11P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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A particular function y = f ( x ) that satisfy the differential equation d y d x = x e − x and the initial condition is y ( 0 ) = 1 .

Solution Summary: The author explains how the differential equation dys=xe-x 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=xe−x and the initial condition is y(0)=1 .

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Chapter 1 Solutions