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If , prove that . [Analysis]
If $y = (x + \sqrt{a^2 + x^2})^m$, prove that $(a^2 + x^2)\frac{d^2y}{dx^2} + x\frac{dy}{dx} - m^2y = 0$. [Analysis]
Given: y = (x + \sqrt{a^2 + x^2})^m
To show: (a^2 + x^2)\frac{d^2y}{dx^2} + x\frac{dy}{dx} - m^2y = 0
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From ISC 2025 Specimen Mathematics Paper 1, question 9(ii).