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If , show that

Mathematics20244 marksDerivation
If $y = 3\cos(\log x) + 4\sin(\log x)$, show that $x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + y = 0$

Given: $y = 3\cos(\log x) + 4\sin(\log x)$

To show: $x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + y = 0$

Answer

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Continuity, Differentiability and Differentiation

From ISC 2024 Mathematics Paper 1, question 7.