Explanation Given information: The given differential equation is ( − y 5 + x 2 y ) d x + ( 2 x y 4 − 2 x 3 ) d y = 0 and integral factor is u ( x , y ) = x − 2 y − 3 . Concept Used: 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: Firstly we multiply the given differential equation by u ( x , y ) = x − 2 y − 3 to produce the exact differential equation. ( − y 5 + x 2 y ) ( x − 2 y − 3 ) d x + ( 2 x y 4 − 2 x 3 ) ( x − 2 y − 3 ) d y = 0 ( − x − 2 y 2 + y − 2 ) d x + ( 2 x − 1 y − 2 x y − 3 ) d y = 0 Now we can compare the differential equation ( − x − 2 y 2 + y − 2 ) d x + ( 2 x − 1 y − 2 x y − 3 ) d y = 0 with the M ( x , y ) d x + N ( x , y ) d y = 0

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ISBN: 9781337604796

Author: Larson

Publisher: CENGAGE L

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Chapter 16.1, Problem 35E

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The general solution of the differential equation (−y5+x2y)dx+(2xy4−2x3)dy=0 using the integral factor u(x,y)=x−2y−3.

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Chapter 16.1, Problem 34E

Chapter 16.1, Problem 36E

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The general solution of the differential equation ( − y 5 + x 2 y ) d x + ( 2 x y 4 − 2 x 3 ) d y = 0 using the integral factor u ( x , y ) = x − 2 y − 3 .

Solution Summary: The author explains how to determine the general solution of the differential equation (-y5+x2

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The general solution of the differential equation (−y5+x2y)dx+(2xy4−2x3)dy=0 using the integral factor u(x,y)=x−2y−3.

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