Program Explanation Given information: Differential equation is ( 1 + 2 x y ) d y d x = 1 + y 2 Formula used: If differential equation is, x ′ + p ( y ) x = q ( y ) Then integrating factor is, I . F . = e ∫ p ( y ) d y Then general solution of the differential equation is, x ( I . F . ) = ∫ q ( y ) ( I . F . ) d y + C Calculation: Consider, given differential equation as, ( 1 + 2 x y ) d y d x = 1 + y 2 ..........(1) This equation can be rewritten as, ( 1 + 2 x y ) = ( 1 + y 2 ) d x d y d x d y − 2 y 1 + y 2 x = 1 1 + y 2 ..........(2) Now, integrating factor of the equation is, I . F . = e − ∫ 2 y 1 + y 2 d y = e − ln ( 1 + y 2 ) = 1 1 + y 2 Now, general solution of the equation is, x ( 1 1 + y 2 ) = ∫ 1 1 + y 2 ( 1 1 + y 2 ) d y + C = ∫ ( 1 1 + y 2 ) 2 d y + C Let, y = tan θ d y = sec 2 θ d θ Then ∫ ( 1 1 + y 2 ) 2 d y = ∫ 1 ( 1 + tan 2 θ ) 2 × sec 2 θ d θ = ∫ 1 sec 4 θ × sec 2 θ d θ = ∫ 1 sec 2 θ d θ =

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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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 1.5, Problem 28P

Program Plan Intro

To find: The general solution of the differential equation (1+2xy)dydx=1+y2 assuming y as the independent variable rather than x.

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Chapter 1.5, Problem 27P

Chapter 1.5, Problem 29P

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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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The general solution of the differential equation ( 1 + 2 x y ) d y d x = 1 + y 2 assuming y as the independent variable rather than x.

Solution Summary: The author explains how the general solution of the differential equation can be rewritten as, cI.F.

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To find: The general solution of the differential equation (1+2xy)dydx=1+y2 assuming y as the independent variable rather than x.

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Chapter 1 Solutions