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

Solution of the differential equation\[x=1+xy\frac{dy}{dx}+\frac{{{x}^

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

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

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