`(dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))`

If y=sin(2sin^(-1)x) , show that: (dy)/(dx)=2sqrt((1-y^(2))/(1-x^(2))) .

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

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)

Solve the differential equation (dy/dx) = (sqrt(1-y^2))/(sqrt(1-x^2))

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

General solution of (dy)/(dx)-(sqrt(1-y^(2)))/(sqrt(1-x^(2)))=0 is

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