If `xy=a[y+sqrt(y^(2)-x^(2))]`, prove that,
`x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))`

If y=(x)/(sqrt(1+x^(2))) , prove that, x^(3)(dy)/(dx)=y^(3) .

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

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

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

(x^(2)+xy)(dy)/(dx)=x^(2)+y^(2)

If sqrt(1-x^(4))+sqrt(1-y^(4))=k(x^(2)-y^(2)) , prove that, (dy)/(dx)=(xsqrt(1-y^(4)))/(ysqrt(1-x^(4)))

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

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

if y = (x+sqrt(x^2+a^2))^n then prove that (dy)/(dx)= (ny)/(sqrt(x^2+a^2)

If y=xlog (x/(a+bx)) , prove that x^3(d^2y)/(dx^2)=(y-xdy/dx)^2 .