# If y = log [x + √x^2+1], then prove that (x^2 + 1)d^2y/dx^2+x(dy/dx)=0  ​

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If y = log [x + $\sqrt{x^2+1}$], then prove that (x2 + 1) $\frac{d^2y}{dx^2}+x\frac{dy}{dx}=0$

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Given,

y = log [x + $\sqrt{x^2+1}$],

Differentiating with respect to x, we get

Differentiating again with respect to x, we get