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If then show that
If $x = \tan\left(\frac{1}{a}\log y\right)$ then show that $(1 + x^2)\frac{d^2y}{dx^2} + (2x - a)\frac{dy}{dx} = 0$
Given: x = \tan\left(\frac{1}{a} \log y\right)
To show: (1 + x^2)\frac{d^2 y}{dx^2} + (2x - a)\frac{dy}{dx} = 0
Answer
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From ISC 2025 Mathematics Paper 1, question 9(i).