Explanation Given information: The given differential equation is ( 10 x + 8 y + 2 ) d x + ( 8 x + 5 y + 2 ) d y = 0 . Concept Used: 1) Let M and N have continuous partial derivatives on an open disk R . The differential equation M ( x , y ) d x + N ( x , y ) d y = 0 is exact if and only if ∂ M ∂ y = ∂ N ∂ x 2) The equation M ( x , y ) d x + N ( x , y ) d y = 0 is an exact differential equation when there exists a function f of two variables x and y having continuous partial derivatives such that f x ( x , y ) = M ( x , y ) and f y ( x , y ) = N ( x , y ) The general solution of the equation is f y ( x , y ) = C Calculation: First we will compare differential equation ( 10 x + 8 y + 2 ) d x + ( 8 x + 5 y + 2 ) d y = 0 with the M ( x , y ) d x + N ( x , y ) d y = 0 . We have M = 10 x + 8 y + 2 N = 8 x + 5 y + 2 ∂ M ∂ y = ∂ ( 10 x + 8 y + 2 ) ∂ y ∂ M ∂ y = 8 ∂ N ∂ x = ∂ ( 8 x + 5 y + 2 ) ∂ x ∂ N ∂ x = 8 Since ∂ M ∂ y = ∂ N ∂ x , hence this differential equation is exact

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ISBN: 8220103600781

Author: Edwards

Publisher: YUZU

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Chapter 16, Problem 3RE

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Whether the differential equation (10x+8y+2)dx+(8x+5y+2)dy=0 is exact or not and also finds the general solution.

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Chapter 16, Problem 2RE

Chapter 16, Problem 4RE

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Chapter 16 Solutions

EBK MULTIVARIABLE CALCULUS

Ch. 16.1 - Exactness What does it mean for the...Ch. 16.1 - Integrating Factor When is it beneficial to use an...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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Whether the differential equation ( 10 x + 8 y + 2 ) d x + ( 8 x + 5 y + 2 ) d y = 0 is exact or not and also finds the general solution.

Solution Summary: The author explains that the differential equation (10x+8y+2)dx + (8x+1,5y)=0 is exact. The general solution is 16x

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Whether the differential equation (10x+8y+2)dx+(8x+5y+2)dy=0 is exact or not and also finds the general solution.

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Chapter 16 Solutions