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

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

Find the equation to the curve passing through (2,2) and having its slope (-(x+y)/x) at the point (x,y)

Find the equation of the line passing through (1,1) and parallel to the line 2x-3y+5=0.

Find the equation of a curve passing through the point (0,0) and whose differential equation is y' = e^(x) sin x .

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

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equation of a curve passing through the point (0, -2) given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Find the equation of a curve passing through the point (0,1).If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

The slope of the tangent at (x, y) to a curve passing through (1, (pi)/(4) ) is given by (y)/(x) - cos^(2) ((y)/(x)) , then the equation of the curve is-

Find the equation of the circle passing through the points of intersection of the circles x^(2) + y^(2) - x + 7y - 3 = 0, x^(2) + y^(2) - 5x - y + 1 = 0 and having its centre on the line x+y = 0.