Word Count : 531

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(i) समीकरण है: [ x , dx + y , dy + 4y^3(x^2 + y^2) , dy = 0 ] इसे पहले व्यवस्थित करें: [ x , dx + y(1 + 4y^2(x^2 + y^2)) , dy = 0 ] या फिर: [ x , dx + y , dy + 4y^3(x^2 + y^2) , dy = 0 ] ध्यान दें कि (y , dy + 4y^3(x^2 + y^2) , dy = y(1 + 4y^2(x^2 + y^2)) , dy) इसे अलग करें: [ x , dx + y(1 + 4y^2(x^2 + y^2)) , dy = 0 ] हम देखते हैं कि यह समीकरण ((x^2 + y^2 + y^4(x^2 + y^2))' = ?) के रूप में लिखा जा सकता है। मान लें (r^2 = x^2 + y^2)। तब (dr^2 = 2x dx + 2y ___ ___ _______ ___ ___ ______ ___ __________ ______ ______ _________ _____.
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