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If , then prove that .
If $y = (x + \sqrt{1 + x^2})^n$, then prove that $(1 + x^2) \frac{d^2y}{dx^2} + x \frac{dy}{dx} = n^2 y$.
Given: $y = (x + \sqrt{1 + x^2})^n$
To show: $(1 + x^2) \frac{d^2y}{dx^2} + x \frac{dy}{dx} = n^2 y$
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From ISC 2023 Specimen Mathematics Paper 1, question 8.