The differential equation representing the family of curves y2=2cx+c, where c is positive parameter, is of

y 2 = 2 c x + c 2 y d y d x = 2 c y 2 = 2 y d y d x x + y d y d x y − 2 x d y d x 2 = 4 y d y d x 3

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The differential equation representing the family of curves $y^{2} = 2 c (x + \sqrt{c})$ , where c is positive parameter, is of

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answer is B, C.

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$y^{2} = 2 c (x + \sqrt{c})$

$2 y \frac{d y}{d x} = 2 c$

$y^{2} = 2 y \frac{d y}{d x} (x + \sqrt{y \frac{d y}{d x}})$

${(y - 2 x \frac{d y}{d x})}^{2} = 4 y {(\frac{d y}{d x})}^{3}$

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