The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\], where a is an arbitrary constant, is

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\]

\[y\text{ }\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]

\[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]

\[{{\left( \frac{dy}{dx} \right)}^{3}}+3\,\frac{dy}{dx}+y=0\]

The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\

1.	The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\], where a is an arbitrary constant, is
A.	\[y\text{ }\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]
B.	\[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]
C.	\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\]
D.	\[{{\left( \frac{dy}{dx} \right)}^{3}}+3\,\frac{dy}{dx}+y=0\]
Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\]

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The differential equation of the family of curves \[{{y}^{2}}=4a(x+a)\], where a is an arbitrary constant, is

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