Program Explanation Given information: The differential equation is ( 4 x − y ) d x + ( 6 y − x ) 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 ) = 4 x − y N ( x , y ) = 6 y − x Substitute 4 x − y for M and 6 y − x for N in equation (1) as, ∂ ∂ y ( 4 x − y ) = ? ∂ ∂ x ( 6 y − x ) 0 − 1 = ? 0 − 1 − 1 = − 1 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 above equation are integrated with respect to x as, ∫ M ( x , y ) d x = F ( x , y ) Substitute 4 x − y in for M ( x , y ) in above equation as, F ( x , y ) = ∫ ( 4 x − y ) d x = 4

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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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 32P

Program Plan Intro

To show: That the differential equation (4x−y)dx+(6y−x)dy=0 and find the solution for it.

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Chapter 1.6, Problem 31P

Chapter 1.6, Problem 33P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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That the differential equation ( 4 x − y ) d x + ( 6 y − x ) d y = 0 and find the solution for it.

Solution Summary: The author explains that the differential equation (4x-y)dx+ (6y-x ) is exact if the below condition satisfies.

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To show: That the differential equation (4x−y)dx+(6y−x)dy=0 and find the solution for it.

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Chapter 1 Solutions