An equation of the curve satisfying `x dy - y dx = sqrt(x^(2)-y^(2))dx` and y(1) = 0 is

An equation of the curve satisfying xdy - ydx = sqrt(x^(2) - y^(2))dx and y(1) = 0 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

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 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 y(x+y^3)dx=x(y^3-x)dy and passing through the point (1,1) is