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in Continuity and Differentiability by (37.2k points)
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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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  y = (x+\(\sqrt{1+x^2})^n\)

Differentiating with respect to x, we get

Again differentiating with respect to x, we get

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