What is the differential equation of a family of parabolas with the foci at the origin and axis along the X-axis?

What is the differential equation of a family of parabolas with the foci at the origin and axis along the X-axis? Correct Answer 2xy’+ y(y’)2-y=0

The equation is, y2=4ax+4a2……………………………………. (1) Differentiating (1) with respect to x, we get, 2yy’=4a ………………………………………………………………………………………….. (2) Therefore, substituting the value of 4a in (1), we get, y2=2yy’x+(yy’)2 So, the required differential equation is given by, 2xy’+y(y’)2-y=0
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