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Let y=f(x)be curve passing through (1,sq...

Let y=f(x)be curve passing through `(1,sqrt3)` such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

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The correct Answer is:
`x+f(x)f'(x)=sqrt(x^(2)+f^(2)(x))andf^(2)(x)=1+2x`
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