Given: `y.sqrt(x^(2)+1)=log{sqrt(x^(2)+1)-x}." ...(i)"`
On differentiating both sides of (i) w.r.t. x, we get
`y.(1)/(2)(x^(2)+1)^(-1//2).2x+(sqrt(x^(2)+1)).(dy)/(dx)`
`=(1)/({sqrt(x^(2)+1)-x}).{(1)/(2)(x^(2)+1)^(-1//2).2x-1}`
`rArr(xy)/(sqrt(x^(2)+1))+(sqrt(x^(2)+1))(dy)/(dx)=(1)/({sqrt(x^(2)+1)-x}).{(x)/(sqrt(x^(2)+1))=-1}`
`rArr(xy)/(sqrt(x^(2)+1))+(sqrt(x^(2)+1))(dy)/(dx)=(1)/({sqrt(x^(2)+1)-x}).({x-sqrt(x^(2)+1)})/(sqrt(x^(2)+1))`
`rArrxy+(x^(2)+1)(dy)/(dx)=-1`
`rArr (x^(2)+1) (dy)/(dx)+xy+1=0.`
