A curve `y=f(x)` has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

Explanation

Let `= int 1/x sqrt((1-sqrtx)/(1+sqrtx))dx`


Put `x=cos^2 theta`


`dx=-2sin theta cos theta d theta`


`I=int 1/(cos^2theta)sqrt((1-cos theta)/(1+cos theta)) (-2 sin theta cos theta)d theta`


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