The solution of the differential equation\[\left\{ 1+x\sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)} \right\}dx+\left\{ \sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)}-1 \right\}ydy=0\] is

\[{{x}^{2}}+\frac{{{y}^{2}}}{2}+\frac{1}{3}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{3/2}}=C\]

\[x-\frac{{{y}^{2}}}{3}+\frac{1}{2}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{1/2}}=C\]

\[x-\frac{{{y}^{2}}}{2}+\frac{1}{3}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{3/2}}=C\]

The solution of the differential equation\[\left\{ 1+x\sqrt{\left( {{x

1.	The solution of the differential equation\[\left\{ 1+x\sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)} \right\}dx+\left\{ \sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)}-1 \right\}ydy=0\] is
A.	\[{{x}^{2}}+\frac{{{y}^{2}}}{2}+\frac{1}{3}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{3/2}}=C\]
B.	\[x-\frac{{{y}^{2}}}{3}+\frac{1}{2}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{1/2}}=C\]
C.	\[x-\frac{{{y}^{2}}}{2}+\frac{1}{3}{{\left( {{x}^{2}}+{{y}^{2}} \right)}^{3/2}}=C\]
D.	None of these
Answer» D. None of these

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The solution of the differential equation\[\left\{ 1+x\sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)} \right\}dx+\left\{ \sqrt{\left( {{x}^{2}}+{{y}^{2}} \right)}-1 \right\}ydy=0\] is

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