Word Count : 327

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To solve the initial value problem (IVP): \[ x^2 \frac{dy}{dx} = \cos x - 2xy, \quad y(\pi) = 0, \quad x > 0, \] we will use an integrating factor to solve the linear first-order ordinary differential equation (ODE). --- ### Step 1: Rewrite the ODE in standard form Divide through by \(x^2\) to rewrite the ODE in the standard linear form: \[ \frac{dy}{dx} + \frac{2}{x} y = \frac{\cos x}{x^2}. \] Here, the coefficient of \(y\) is \(P(x) = \frac{2}{x}\), and _____ ____ ______ ___ _________ _____.
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