if y=log [x+root (x^2+a^2) then show that (x^2+a^2)d2y/dx2+xdy/dx=0

Dear student
We have, y=logx+x2+a2Differentiating wrt xdydx=1x+x2+a2×ddxx+x2+a2=1x+x2+a21+2x2x2+a2dydx=1x+x2+a2×x+x2+a2x2+a2y1=1x2+a2, where y1=dydxy12x2+a2=1Differentiating wrt x we gety12ddxx2+a2+x2+a2.ddxy12=0y12.2x+x2+a2+2y1y2=02y1y2x2+a2+xy1=0  y10
Regards

  • -1
What are you looking for?