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A family of curves has the differential equation $xy \large\frac{dy}{dx}$$=2y^2-x^2$. Then the family of curves is :

\[\begin {array} {1 1} (1)\;y^2=cx^2+x^3 & \quad (2)\;y^2=cx^4+x^3 \\ (3)\;y^2=x+cx^4 & \quad (4)\;y^2=x^2+cx^4 \end {array}\]

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$ (3)\;y^2=x+cx^4$
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