If y=x3 log⁡(1/x), then prove that x (d2 y)+(dx2 ) - 2 dy/dx+3x2=0.

Dear Student,

Please find below the solution to the asked query:
y=x3log1xProve that xd2ydx2-2dydx+3x2=0dydx=x311x-1x2+log1x3x2=-x2+3x2log1xd2ydx2=-2x+6xlog1x+3x2×x×-1x2d2ydx2=-5x+6xlog1xNow put the values xd2ydx2-2dydx+3x2x-5x+6xlog1x-2-x2+3x2log1x+3x2-5x2+6x2log1x+2x2-6x2log1x+3x2-5x2+2x2+3x20 Hence Proved

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