Solve the following differential equation:+ y = x - x. - Vidyadip

Question

Solve the following differential equation:$+ y = \cos x - \sin x.$

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Answer

Getting integrating factor $ = e \int^{1 dx} = e^{x}$$\therefore \text{Solution is y.} e^{x} = \int(\cos x- \sin x) e^{x} dx$
$\text{Unsing} \int\text{[f(x) +f'(x)]} e^{x} + \text{c we get }$
$y.e^{x} = \cos \text{x e}^{x} + c$
$\text{or y} = \cos x + \text{c e}^{-x} $

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