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

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

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

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

The equation of the curve satisfying the differential equation y^(2)(x^(2)+1)=2xy passing through the point (0,1) and having slope of tangnet at x=0 as 3, is (Here y=(dy)/(dx) and y_(2)=(d^(2)y)/(dx^(2)))