If `ysqrt(x^(2)+1)=log(sqrt(x^(2)+1)-x)`, show that,
`(x^(2)+1)(dy)/(dx)+xy+1=0`

If y sqrt(x^(2)+1)=log(sqrt(x^(2)+1)-x) , show that, (x^(2)+1)(dy)/(dx)+xy+1=0

answeer the following : (i) if y sqrt(x^2+1)=log(sqrt(x^2+1)-x) , show that , (x^2+1) dy/dx +xy+1=0

If y=[log(x+sqrt(x^2+1))]^2 , show that, (1+x^2)(d^2y)/(dx^2)+xdy/dx=2

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)) , show that, (1-x^(2))^(2)(D^(2)y)/(dx^(2))-3x(1-x^(2)))(dy)/(dx)=1

xsqrt(y^(2)-1)dx-ysqrt(x^(2)-1)dy=0

If y=(x^(2))/(2)+(x)/(2) sqrt(x^(2)+1)+log sqrt(x+sqrt(x^(2)+1)) , prove that, 2y=x (dy)/(dx)+log((dy)/(dx))

If y=sqrt((1-x)/(1+x)) , prove that , (1-x^(2)) (dy)/(dx)+y=0

(x^(2)+ 1) dy/dx+ 2xy = 4x^(2)

If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo) , show that, x (dy)/(dx)=(y^(2))/(2-y log x).

If y=log(x+sqrt(x^2+a^2)) , show that (a^2+x^2)y_2+xy_1=0