Question

If `ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=0`

Answer 1

`ysqrt(x^(2)+1)=log{(sqrt(x^(2)+1)-x}`
Differentiating both sides w.r.t. x, we get
`(dy)/(dx)sqrt(x^(2)+1)+y(1)/(2sqrt(x^(2)+1))2x=(1)/(sqrt(x^(2)+1)-x)xx{(1)/(2)(2x)/(sqrt(x^(2)+1))-1}`
`"or "(x^(2)+1)(dy)/(dx)+xy=sqrt(x^(2)+1)(-1)/(sqrt(x^(2))+1)`
`"or "(x^(2)+1)(dy)/(dx)+xy+1=0`