y= xx P.T d2y/dx2 - 1/y(dy/dx)2 - y/x =0

Dear Student,
Please find below the solution to the asked query:

We have:y=xx;ilogy=logxxlogy=x.logx1y.dydx=x.ddxlogx+logx.ddxxdydx=yx.1x+logxdydx=xx1+logx ;iiAgain differentiating with respect to x we get:d2ydx2=xx.ddx1+logx +1+logx.ddxxxd2ydx2=xx1x+1+logx.xx1+logx Using iid2ydx2=xxx+xx1+logx2 ;iiiL.H.S.=d2ydx2-1ydydx2-yxUsing i,ii and iii, we get:L.H.S.=xxx+xx1+logx2-1xxxx1+logx2-xxx=xx1+logx2-xx.xxxx1+logx2=xx1+logx2-xx1+logx2=0=R.H.S. Hence proved

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