Solution of the differential equation \[(y+x\sqrt{xy}(x+y))\,dx+(y\sqrt{xy}(x+y)-x)dy=0\] is

\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\cot }^{-1}}\sqrt{\frac{x}{y}=c}\]

\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+{{\tan }^{-1}}\sqrt{\frac{y}{x}=c}\]

\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\tan }^{-1}}\sqrt{\frac{x}{y}=c}\]

Solution of the differential equation \[(y+x\sqrt{xy}(x+y))\,dx+(y\sqr

1.	Solution of the differential equation \[(y+x\sqrt{xy}(x+y))\,dx+(y\sqrt{xy}(x+y)-x)dy=0\] is
A.	\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+{{\tan }^{-1}}\sqrt{\frac{y}{x}=c}\]
B.	\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\tan }^{-1}}\sqrt{\frac{x}{y}=c}\]
C.	\[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\cot }^{-1}}\sqrt{\frac{x}{y}=c}\]
D.	None of these
Answer» C. \[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\cot }^{-1}}\sqrt{\frac{x}{y}=c}\]

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Solution of the differential equation \[(y+x\sqrt{xy}(x+y))\,dx+(y\sqrt{xy}(x+y)-x)dy=0\] is

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