If `y={x+sqrt(x^2+1)}^m` , show that `(x^2+1)y_2+x y_1-m^2\ y=0`

Explanation

To solve the problem, we need to show that

\[ (x^2 + 1)y_2 + xy_1 - m^2 y = 0 \]

where \( y = (x + \sqrt{x^2 + 1})^m \), \( y_1 = \frac{dy}{dx} \) (the first derivative), and \( y_2 = \frac{d^2y}{dx^2} \) (the second derivative).

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