sqrt(1-x^(6))dy=x^(2)dx

If sqrt((1-x^(6)))+sqrt((1-y^(6)))=a(x^(3)-y^(3)) , a is constant and (dy)/(dx)=f(x,y) sqrt(((1-y^(6))/(1-x^(6)))) , then

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

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

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

If y=sqrt(x+1)+sqrt(x-1)," then: "2sqrt(x^(2)-1)*(dy)/(dx)=

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)