Explanation Definition used: The first order linear equation in the standard form d y d t + p ( t ) y = g ( t ) where p and g are given functions of the independent variable t . Calculation: Given that, the differential equation d y d x + 2 y = e − x 2 − 2 x , y ( 0 ) = 3 . Here, p = 2 , g = e − x 2 − 2 x . Obtain the integrating factor μ ( x ) as, μ ( x ) = e ∫ 2 d x = e 2 x Multiply the equation d y d x + 2 y = e − x 2 − 2 x with the integrating factor e 2 x as, e 2 x d y d x + 2 y e 2 x = e 2 x ( e − x 2 − 2 x ) e 2 x d y d x + 2 y e 2 x = e − x 2 − 2 x + 2 x e 2 x d y d x + 2 y e 2 x = e − x 2 d ( e 2 x y ) = e − x 2

Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion

11th Edition

ISBN: 9781119336617

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley (WileyPLUS Products)

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Chapter 2, Problem 15MP

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The solution of the differential equation dydx+2y=e−x2−2x,y(0)=3.

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Chapter 2, Problem 14MP

Chapter 2, Problem 16MP

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Chapter 2 Solutions

Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion

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The solution of the differential equation d y d x + 2 y = e − x 2 − 2 x , y ( 0 ) = 3 .

The solution of the differential equation dydx+2y=e−x2−2x,y(0)=3.

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Chapter 2 Solutions