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

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

Let the curve y = f (x) satisfies the equation (dy)/(dx)=1-1/x^2 and passes through the point (2,7/2) then the value of f(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)andy_2=(d^2y)/(dx^2))

A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^2)/(x^2y-y) and passes through (0,0) (1) The equation of the curve is x^2+y^2+2x=x^2y^2 (2) The equation of the curve is x^2+y^2+2x+2y=x^2y^2 (3) x=0 is a tangent to curve (4) y=0 is a tangent to curve

Solve the differential equation (dy)/(dx)=(2y-6x-4)/(y-3x+3).

The foci of the curve which satisfies the equation (1+y^(2))dx - xy dy = 0 and passes through the point (1, 0) are

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