The differential equation of a family of parabolas with axis parallel to the axis of $y$ is ${(x - a)}^{2} = A (y - b)$ solve.

y_{2} = 2 y_{1} + x

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y_{3} = 2 y_{1}

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y_{2}^{3} = y_{1}

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None of these

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Solution

The correct option is B None of these
The equation of the family of parabolas with axis parallel to axis of $y$ is
${(x - a)}^{2} = A (y - b)$
On differentiating w,r,t, $x$ , we get
$2 (x - a) = A y_{1}$
Again differentiating w.r.t $x$ we get
$2 = A y_{2}$
On again differentiating w.r.t. $x$ we get
$y_{3} = 0$

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