Program Explanation Given information: The differential equation is 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) y ′ = 0 . Explanation: The given differential equation can be written as, 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) d y d x = 0 ( 6 x y 3 + 2 y 4 ) d x + ( 9 x 2 y 2 + 8 x y 3 ) d y = 0 The general form of exact 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) 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 ) = 6 x y 3 + 2 y 4 N ( x , y ) = 9 x 2 y 2 + 8 x y 3 Substitute 6 x y 3 + 2 y 4 for M and 9 x 2 y 2 + 8 x y 3 for N in equation (1) as, ∂ ∂ y ( 6 x y 3 + 2 y 4 ) = ? ∂ ∂ x ( 9 x 2 y 2 + 8 x y 3 ) 6 x ⋅ 3 y 2 + 8 y 3 = ? 9 y 2 ⋅ 2 x + 8 y 3 18 x y 2 + 8 y 3 = 18 x y 2 + 8 y 3 Thus, the given differential equation is exact

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.

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Chapter 1, Problem 12RP

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Program Description: Purpose of problem is to calculate the general solution of the differential equation 6xy3+2y4+(9x2y2+8xy3)y′=0 .

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Chapter 1, Problem 11RP

Chapter 1, Problem 13RP

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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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Program Description: Purpose of problem is to calculate the general solution of the differential equation 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) y ′ = 0 .

Solution Summary: The author explains the purpose of the problem, which is to calculate the general solution to the differential equation.

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Program Description: Purpose of problem is to calculate the general solution of the differential equation 6xy3+2y4+(9x2y2+8xy3)y′=0 .

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Chapter 1 Solutions