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

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

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

Solution Summary: The author explains how the differential equation (2x+y-3)dx + (x-3y+1 ) satisfies the initial condition y(2)=0.

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

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