If `y=x+1/x` , then `xdy/dx+y` is equal to

If x^y=y^x , then (dy)/(dx) is equal to......

If y^(x) = x^(y) , "then" (dy)/(dx) is equal to

If the curve , y = y(x) represented by the solution of the differential equation (2xy^2-y)dx+xdy=0 , passes through the intersection of the lines , 2x-3y=1 and 3x+2y=8 , then |y(1)| is equal to _______ .

If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

Let y = y (x) be the solution of the differential equation xdy = (y + x^3 cos x)dx with y( pi ) = 0, then y ((pi)/(2)) is equal to