# If y = (x+√(1+x^2))^n, then show that (1+x^2) d^2y/dx^2+x(dy/dx)=n^2y

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If y = (x+$\sqrt{1+x^2})^n$, then show that (1+x2)$\frac{d^2}{dx^2}+x\frac{dy}{dx}=n^2y$

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Given,

y = (x+$\sqrt{1+x^2})^n$

Differentiating with respect to x, we get

Again differentiating with respect to x, we get