Program Explanation Given information: The differential equation is, ( 1 + y e x y ) d x + ( 2 y + x e x y ) d y = 0 Concept used: The general differential equation is, M ( x , y ) d x + N ( x , y ) d y = 0 The above differential equation is exact if and only if the below condition satisfies, ∂ M d y = ∂ N ∂ x ....... (1) Calculation: Compare the given differential equation with the general differential equation to obtain the value of M ( x , y ) and N ( x , y ) as M ( x , y ) = 1 + y e x y N ( x , y ) = 2 y + x e x y Substitute 1 + y e x y for M and 2 y + x e x y for N in equation (1) as ∂ ∂ y ( 1 + y e x y ) = ? ∂ ∂ x ( 2 y + x e x y ) 0 + e x y + y x e x y = ? 0 + e x y + x y e x y e x y + y x e x y = e x y + y x e x y Thus, the given differential equation is exact. The value of M ( x , y ) can be written as M ( x , y ) = ∂ F ∂ x The value of F ( x , y ) can be obtained if both the sides of the above equation are integrated with respect to x as ∫ M ( x , y ) d x = F ( x , y ) Substitute 1 + y e x y in for M ( x , y ) in the above equationas F ( x , y ) =

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 1.6, Problem 36P

Program Plan Intro

To show: Differential equation (1+yexy)dx+(2y+xexy)dy=0 and find the solution for it.

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Chapter 1.6, Problem 35P

Chapter 1.6, Problem 37P

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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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Differential equation ( 1 + y e x y ) d x + ( 2 y + x e x y ) d y = 0 and find the solution for it.

Solution Summary: The author explains how to solve the differential equation (1+yexy

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To show: Differential equation (1+yexy)dx+(2y+xexy)dy=0 and find the solution for it.

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Chapter 1 Solutions