Explanation Given: The differential equation 2 d y d x − 4 x y = 5 x . The provided initial condition is y ( 1 ) = 10 . 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 the given differential equation, 2 d y d x − 4 x y = 5 x Divide above differential by 2 from both of the sides, d y d x − 2 x y = 5 2 x (1) Compare above differential with d y d x + P ( x ) y = Q ( x ) . So, get the values P ( x ) = − 2 x and Q ( x ) = 5 2 x . Now, find the integrating factor as I ( x ) = e ∫ p ( x ) d x . I ( x ) = e − 2 ∫ x d x = e − x 2 Multiply each term of equation (1) by I ( x ) . e − x 2 d y d x − 2 e − x 2 x y = 5 2 e − x 2 x The sum of terms on the left can now be replaced with D x ( y ⋅ e − x 2 )

11th Edition

ISBN: 2818440028625

Author: Lial

Publisher: ELSEVIER

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Chapter 10.2, Problem 18E

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

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Chapter 10.2, Problem 17E

Chapter 10.2, Problem 19E

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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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