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If y={log(x+sqrt(x^2+1))}^2 , show that ...

If `y={log(x+sqrt(x^2+1))}^2` , show that `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=0` .

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To solve the problem, we need to show that \[ (1+x^2) \frac{d^2y}{dx^2} + x \frac{dy}{dx} = 0 \] given that ...
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