Word Count : 315

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प्राचल विचरण विधि (Method of Variation of Parameters) का उपयोग करके समीकरण को हल करने के लिए, हम निम्नलिखित चरणों का अनुसरण करेंगे: #### दिया गया समीकरण: \[ (1+x)^2 \frac{d^2y}{dx^2} + (1+x) \frac{dy}{dx} + y = 4 \cos(\ln(1+x)) \] यह एक द्वितीय कोटि की रैखिक अवकल समीकरण (Second-order Linear Differential Equation) है। --- ### चरण 1: सहगामी समीकरण (Homogeneous Equation) हल करें संबंधित समरूप समीकरण (Homogeneous Equation) है: \[ (1+x)^2 \frac{d^2y}{dx^2} + (1+x) \frac{dy}{dx} + y = 0 _______ _________ _______ _____ ________ ___ _____ _________ _______ _____ ________.
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