Explanation:tion of the differential equation x d x+ y d y x d x- y d y = y^ 3 x^ 3 is…

Mathematics · JEE Advanced · NTA Exams — Differential Equations

1. \(\frac{3}{2} \log \left(\frac{y}{x}\right)+\log \left|\frac{x^{3 / 2}+y^{3 / 2}}{x^{3 / 2}}\right|+\tan ^{-1}\left(\frac{y}{x}\right)^{3 / 2}+c=0\)
2. \(\frac{2}{3} \log \left(\frac{y}{x}\right)+\log \left|\frac{x^{3 / 2}+y^{3 / 2}}{x^{3 / 2}}\right|+\tan ^{-1} \frac{y}{x}+c=0\)
3. \(\frac{2}{3} \log \left(\frac{\mathrm{y}}{\mathrm{x}}\right)+\log \left(\frac{\mathrm{x}+\mathrm{y}}{\mathrm{x}}\right)+\tan ^{-1}\left(\frac{\mathrm{y}^{3 / 2}}{\mathrm{x}^{3 / 2}}\right)+\mathrm{c}=0\)
4. none of the above

Answer

(D) none of the above

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