Word Count : 664

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हमारी दी गई अवकल समीकरण है: $$ (2yx^2 + 4)\frac{dy}{dx} + (2y^2x - 3) = 0 $$ चरण 1: समीकरण को मानक रूप में लाएँ पहले हम समीकरण को इस प्रकार लिखें: $$ (2yx^2 + 4)\frac{dy}{dx} = - (2y^2x - 3) $$ अब इसे व्यवस्थित करें: $$ \frac{dy}{dx} = \frac{ - (2y^2x - 3) }{ 2yx^2 + 4 } $$ चरण 2: चर पृथक्करण विधि (Separation of Variables) हम प्रयास करेंगे इसे $x$ और $y$ के पदों में विभाजित करने का। समीकरण को थोड़ा सरल करते हैं। हर पद में से $2$ सामान्य रूप में निकालें: $$ \frac{dy}{dx} = \frac{ -2(y^2x - \frac{3}{2}) }{ 2(yx^2 + 2) } = \frac{ - (y^2x - \frac{3}{2}) }{ yx^2 + 2 } $$ अब हमारे पास है: $$ \frac{dy}{dx} = \frac{ - (y^2x - \frac{3}{2}) }{ yx^2 + 2 } $$ यह अब भी सीधा चर पृथक्करण योग्य नहीं दिख रहा है। इसलिए हम एक और विधि अपनाते हैं — चलिए उपपत्ति द्वारा हल करते हैं। चरण 3: चलिए ______ ______ ___ ________ ____ _______ ________ ________.
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