If , then prove that .
If $y = x^3 \log\left(\frac{1}{x}\right)$, then prove that $x\frac{d^2 y}{dx^2} - 2\frac{dy}{dx} + 3x^2 = 0$.
Given: $y = x^3 \log\left(\frac{1}{x}\right)$
To show: $x\frac{d^2 y}{dx^2} - 2\frac{dy}{dx} + 3x^2 = 0$
Answer
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From ISC 2026 Mathematics Paper 1, question 9.