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

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

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

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

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

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

If y=log(x+sqrt(1+x^(2))), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log[x+sqrt(x^(2)+1)], prove that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log[x+sqrt(x^(2)+1)] , then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=0 .

If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(dx)=0