Word Count : 369

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We need to solve the first-order linear differential equation: \[ \sin x \frac{dy}{dx} + y \cos x = 1 \] ### Step 1: Convert to Standard Form The standard form of a first-order linear differential equation is: \[ \frac{dy}{dx} + P(x)y = Q(x) \] Dividing the entire equation by \(\sin x\), we get: \[ \frac{dy}{dx} + \frac{\cos x}{\sin x} y = \frac{1}{\sin x} \] So, here: \[ P(x) = \frac{\cos x}{\sin x}, \quad ____ _______ ______ _________ _______ ______ ___ ________ ___ ___.
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