Explanation Given information: The given differential equation is ( 2 x y − 9 x 2 ) d x + ( 2 y + x 2 + 1 ) d y = 0 with initial condition y ( 0 ) = − 3 . 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 ( 2 x y − 9 x 2 ) d x + ( 2 y + x 2 + 1 ) d y = 0 with the M ( x , y ) d x + N ( x , y ) d y = 0 . We have M = 2 x y − 9 x 2 N = 2 y + x 2 + 1 ∂ M ∂ y = ∂ ( 2 x y − 9 x 2 ) ∂ y ∂ M ∂ y = 2 x ∂ N ∂ x = ∂ ( 2 y + x 2 + 1 ) ∂ x ∂ N ∂ x = 2 x Since ∂ M ∂ y = ∂ N ∂ x , hence this differential equation is exact

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ISBN: 9781337604796

Author: Larson

Publisher: CENGAGE L

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Chapter 16.1, Problem 17E

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The particular solution of the differential equation (2xy−9x2)dx+(2y+x2+1)dy=0 that satisfies the initial condition y(0)=−3.

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Chapter 16.1, Problem 16E

Chapter 16.1, Problem 18E

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The particular solution of the differential equation ( 2 x y − 9 x 2 ) d x + ( 2 y + x 2 + 1 ) d y = 0 that satisfies the initial condition y ( 0 ) = − 3 .

Solution Summary: The author explains how the differential equation (2xy-9x2)dx+ left (2y+

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The particular solution of the differential equation (2xy−9x2)dx+(2y+x2+1)dy=0 that satisfies the initial condition y(0)=−3.

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Chapter 16 Solutions