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

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))

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

If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfrac(1-y^2)(1-x^2)

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2/y^2sqrt((1-y^6)/(1-x^6))

If sqrt(1-x^4)+sqrt(1-y^4)=k(x^2-y^2) ,show that y_1=(xsqrt(1-y^4))/(ysqrt(1-x^4))

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) .

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