To determine To solve: The given differential equation subject to given initial condition. Explanation Given: The given differential equation is x d y d x + 5 y = x 2 . The provided initial condition is y ( 2 ) = 12 . Concept used: Integrating factor The function I ( x ) = e ∫ p ( x ) d x is called an integrating factor for the differential equation d y d x + P ( x ) y = Q ( x ) . Calculation: Consider, x d y d x + 5 y = x 2 (1) Compare above differential with d y d x + P ( x ) y = Q ( x ) . So, get the values P ( x ) = 5 x and Q ( x ) = x 2 . Now, find the integrating factor as I ( x ) = e ∫ p ( x ) d x . I ( x ) = e 5 ∫ 1 x d x = e 5 ln x = e ln x 5 = x 5 Multiply each term of equation (1) by I ( x ) . x 5 d y d x + 5 x 4 y = x x 5 = x 6 The sum of terms on the left can now be replaced with D x ( y

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 17E

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To solve: The given differential equation subject to given initial condition.

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Chapter 10.2, Problem 16E

Chapter 10.2, Problem 18E

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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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