To determine The general solution of the ordinary differential equation y ′ + y sin x = e cos x with the initial condition y ( 0 ) = − 2.5 . Explanation The given ordinary differential equation is y ′ + y sin x = e cos x . The above differential equation is of the form y ′ + p y = r , where p = sin x and r = e cos x . The general solution is given by, y ( x ) = e − h ( c + ∫ r e h d x ) ... ( 1 ) The integrating factor h is ∫ p d x and it is calculated as follows. ∫ p d x = ∫ sin x d x = − cos x Substitute the integrating factor h in equation (1) and obtain the general solution as follows. y ( x ) = e − ( − cos x ) ( c + ∫ e cos x e − cos x d x ) = e cos x ( c + ∫ e cos x − cos x d x ) = e cos x ( c +

10th Edition

ISBN: 9781119455929

Author: Kreyszig

Publisher: WILEY

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Chapter 1.5, Problem 9P

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The general solution of the ordinary differential equation y′+ysinx=ecosx with the initial condition y(0)=−2.5.

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Chapter 1.5, Problem 8P

Chapter 1.5, Problem 10P

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ADVANCED ENGINEERING MATHEMATICS (LL)

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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