The equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is

Find the equation of a curve passing through (0,1) and having gradient (-(y+y^3))/(1+x+x y^2) at (x , y) .

Find the equation of a curve passing through (1,1) and whose slope of tangent at a point (x, y) is -(x)/(y) .

The equation of the curve passing through the point (1,pi/4) and having a slope of tangent at any point (x,y) as y/x - cos^2(y/x) is

The equation of the curve passing through the point (1,pi/4) and having a slope of tangent at any point (x,y) as y/x - cos^2(y/x) is

The equation of the curve passing through (3, 9) which satisfies dy //dx =x +1//x^2 is :

The equation of the line passing through (1,2) and perpendicular to x+y+7=0 is

The equation of the curve passing through the point (1,1) and satisfying the differential equation (dy)/(dx) = (x+2y-3)/(y-2x+1) is

The equation of the curves through the point (1, 0) and whose slope is (y-1)/(x^2+x) is

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

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