The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is [EAMCET 2003]

\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+y=2xy\frac{dy}{dx}\]

\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+4x\frac{dy}{dx}=4y\]

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

\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+2xy\frac{dy}{dx}+y=0\]

The differential equation of the family of parabolas with focus at the

1.	The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is [EAMCET 2003]
A.	\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+4x\frac{dy}{dx}=4y\]
B.	\[-y\,{{\left( \frac{dy}{dx} \right)}^{2}}=2x\frac{dy}{dx}-y\]
C.	\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+y=2xy\frac{dy}{dx}\]
D.	\[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+2xy\frac{dy}{dx}+y=0\]
Answer» C. \[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+y=2xy\frac{dy}{dx}\]

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The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is [EAMCET 2003]

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