Which of the following are true for the curve represented by the differential equation `sec^2y dy/dx+2x tany=x^3` satisfying `y(1)=0` (A) equation of curve is `2tany=x^2-1` (B) equation of curve is `y^2=x^3-1` (C) curve is a parabola (D) curve is not a conic

The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e^(x) secy satisfying y(1)=0 , is

The curve represented by the differential equation (x^2+y^2+1)dx-2xydy=0 satisfying y(1)=1 is (A) x^2-y^2+x-1=0 (B) (x-1)^2+(y-2)^2=1 (C) a hyperbola (D) a circle

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

The curve amongst the family of curves, represented by the differential equation (x^2-y^2)dx+2xydy=0 which passes through (1,1) is

The curve represented by the differential equation cosy(1-xcosy)dx-sinydy=0 satisyfing y(0)=0 is (A) tany=x^2 (B) secy=x+1 (C) symmetric about x-axis (D) symmetric about y-axis

The differential equation of the curve x/(c-1)+y/(c+1)=1 is

If the curve satisfying differential equation xdy=(y+x^(3))dx passes through (1, 1), then the equation to the curve is

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

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

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