To determine The general solution of the differential equation x d y d x − y − x = 0 , x > 0 . Explanation Given: The differential equation is x d y d x − y − x = 0 , x > 0 . Concept used: Integrating factor: The function I ( x ) = e ∫ P ( x ) d x is called an integrating factor for linear differential equation d y d x + P ( x ) y = Q ( x ) . Calculation: Rewrite the given differential equation x d y d x − y − x = 0 as follows: x d y d x − y − x = 0 x d y d x − y = x d y d x − y x = 1 [ Divide both sides by x ] Compare the equation d y d x − y x = 1 with the linear differential equation d y d x + P ( x ) y = Q ( x ) to obtain the values of P ( x ) and Q ( x ) . P ( x ) = − 1 x Q ( x ) = 1 Substitute − 1 x for P ( x ) in equation I ( x ) = e ∫ P ( x ) d x to obtain the integrating factor I ( x )

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Differential Equations

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Chapter 10.2, Problem 5E

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The general solution of the differential equation xdydx−y−x=0,x>0.

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Chapter 10.2, Problem 4E

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Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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The general solution of the differential equation x d y d x − y − x = 0 , x &gt; 0 .

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The general solution of the differential equation x d y d x − y − x = 0 , x > 0 .