" 5."(1+x^(2))(dy)/(dx)+1+y^(2)=0

If (1+x^(2))(dy)/(dx)=1+y^(2),y(0)=1, then y(2)=

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

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0

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

The solution of the differential equation (1+x^(2))(1+y)dy+(1+x)(1+y^(2))dx=0

IF y=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0 .