Word Count : 291

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To solve the differential equation \[ \sin x \frac{dy}{dx} + y \cos x = 1 \] we will first rewrite it in the standard form of a first-order linear differential equation. We start by isolating \(\frac{dy}{dx}\): \[ \sin x \frac{dy}{dx} + y \cos x = 1 \] Divide through by \(\sin x\): \[ \frac{dy}{dx} + y \cot x = \frac{1}{\sin x} \] Now, we have a linear differential equation of the form: _______ ______ ______ _________ _____ _____.
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