Solution of differential equation \[{{x}^{2}}=1+{{\left( \frac{x}{y} \right)}^{-1}}\frac{dy}{dx}+\frac{{{\left( \frac{x}{y} \right)}^{-2}}{{\left( \frac{dy}{dx} \right)}^{2}}}{2!}\]\[+\frac{{{\left( \frac{x}{y} \right)}^{-3}}{{\left( \frac{dy}{dx} \right)}^{3}}}{3!}+.........\] is

\[{{y}^{2}}={{x}^{2}}(ln\,\,{{x}^{2}}-1)+C\]

\[y={{x}^{2}}{{e}^{{{x}^{2}}}}+C\]

Solution of differential equation \[{{x}^{2}}=1+{{\left( \frac{x}{y} \

1.	Solution of differential equation \[{{x}^{2}}=1+{{\left( \frac{x}{y} \right)}^{-1}}\frac{dy}{dx}+\frac{{{\left( \frac{x}{y} \right)}^{-2}}{{\left( \frac{dy}{dx} \right)}^{2}}}{2!}\]\[+\frac{{{\left( \frac{x}{y} \right)}^{-3}}{{\left( \frac{dy}{dx} \right)}^{3}}}{3!}+.........\] is
A.	\[{{y}^{2}}={{x}^{2}}(ln\,\,{{x}^{2}}-1)+C\]
B.	\[y={{x}^{2}}(ln\,\,x-1)+C\]
C.	\[{{y}^{2}}=x(ln\,\,x-1)+C\]
D.	\[y={{x}^{2}}{{e}^{{{x}^{2}}}}+C\]
Answer» B. \[y={{x}^{2}}(ln\,\,x-1)+C\]

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Solution of differential equation \[{{x}^{2}}=1+{{\left( \frac{x}{y} \right)}^{-1}}\frac{dy}{dx}+\frac{{{\left( \frac{x}{y} \right)}^{-2}}{{\left( \frac{dy}{dx} \right)}^{2}}}{2!}\]\[+\frac{{{\left( \frac{x}{y} \right)}^{-3}}{{\left( \frac{dy}{dx} \right)}^{3}}}{3!}+.........\] is

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