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

Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.


  • 17
What are you looking for?