हल कीजिए `y(1-x^2)(dy)/(dx) = x(1+y^2)`

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

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

If y= (sin^(-1) x)^2 , then (1-x^2) (d^2 y)/(dx^2) - x (dy/dx) = ..........

If y=cos (mcos ^(-1) x ),then (1-x^(2)) (d^(2)y)/(dx^(2) )-x( dy)/(dx)=

If y=sin^(-1)x ,then prove that (1-x^(2))(d^(2)y)/(dx^(2))=x(dy/dx)

(1+x^(2))dy=y^(2)dx

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

y(1+x^(2))dy=x(1+y^(2))dx

If y=sin (msin ^(-1) x),then (1-x^(2))(d^(2)y)/(dx^(2))-x( dy)/(dx)=