The curve satisfying the equation `(dy)/(dx)=(y(x+y^3))/(x(y^3-x))` and passing through the point `(4,-2)` is

The curve satisfying the differential equation (dy)/(dx)=(y(x+y^(3)))/(x(y^(3)-x)) and passing through (4,-2) is

The equation of the curve satisfying the eqution (xy-x^(2)) (dy)/(dx) = y^(2) and passing through the point (-1,1) is

The curve satisfying the equation (x^(2)-y^(2))dx+2xydy=0 and passing through the point (1,1) is

The curve satisfying the differential equation (dx)/(dy) = (x + 2yx^2)/(y-2x^3) and passing through (1, 0) is given by

The equation of the curve satisfying the differential equation (dy)/(dx)+(y)/(x^(2))=(1)/(x^(2)) and passing through ((1)/(2),e^(2)+1) is

The equation of the curve satisfying the differential equation (dy)/(dx)+2(y)/(x^(2))=(2)/(x^(2)) and passing through ((1)/(2),e^(4)+1) is

The equation of the curve satisfying the equation ( 1 + y^2) dx + ( x-e^(-tan^(-1)y))dy=0 and passing through origin is