If `y(x-y)^(2)=x` then `int (dx)/(x-3y)=`

Statement I If y is a function of x such that y(x-y)^(2)= x, then int (dx)/(x-3y)=1/2 [ log (x-y)^(2)-1] Statement II int (dx)/(x-3y)=log (x-3y)+C

If y is implicit differentiable function of x such that y(x+y)^(2)=x then int(dx)/(x+3y)

If y is implicit differentiable function of x such that y(x+y)^(2)=x then int(dx)/(x+3y)

If y=x^(2)+2x+3, then : int((dx)/(dy))dx=

If x^(3)+y^(3)+xy^(2)+x^(2)y-x^(2)-y^(2)=0 then int ydx=

If y^(3) - 3y^(2) x=x^(3) +3x^(2) y,then (dy)/(dx)=

If x ylog(x+y)=1 , prove that (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y))

If x+y=e^(x-y) then show that (d^(2)y)/(dx^(2))=(4(x+y))/((1+x+y)^(3))

If y^3-3x y^2=x^3+3x^2\ y , find (dy)/(dx)