Program Explanation Given information: The differential equation is y ′ = 1 + x + y + x y . Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables, which is done as ∫ d y g ( y ) = ∫ f ( x ) d x Calculation: The given differential equation is y ′ = 1 + x + y + x y . Separate the variables of the above differential equation as d y d x = 1 + x + y ( 1 + x ) d y d x = ( 1 + y ) ( 1 + x ) d y 1 + y = ( 1 + x ) d x Now, integrate the equation on both the sides

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

Publisher: PEARSON

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 1.4, Problem 17P

Program Plan Intro

To find: A general solution of the differential equation y′=1+x+y+xy .

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Chapter 1.4, Problem 16P

Chapter 1.4, Problem 18P

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Chapter 1 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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A general solution of the differential equation y ′ = 1 + x + y + x y .

Solution Summary: The author explains the general implicit solution of the differential equation yprime, which can be calculated with the help of separating the variables.

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To find: A general solution of the differential equation y′=1+x+y+xy .

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Chapter 1 Solutions