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If , prove that

Mathematics20254 marksDerivation
If $x = \sin t, y = \sin pt$, prove that $(1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} + p^2 y = 0$

Given: $x = \sin t, y = \sin pt$

To show: (1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} + p^2 y = 0

Answer

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Continuity, Differentiability and Differentiation

From ISC 2025 Improvement Mathematics Paper 1, question 8(i).