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If \(y = x^3log(\frac{1}{x}),\) then prove that \(x\frac{d^2y}{dx^2}-2\frac{dy}{dx}+3x^2=0.\)

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The given differential equation is

\(y = x^3log(\frac{1}{x}),\)

Again differentiating with respect to x

Hence proved.

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