# If y = x^3log(1/x),  then prove that x(d^2y/dx^2)-2(dy/dx)+3x^2 = 0.  ​

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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.