Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through the point (–2, 3), given that the slope of the tangent to the curve at any point (x, y) is 2x/y^2

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.

Find the equation of a curve passing through the origin if the slope of the tangent to the curve at any point (x,y) is equal to the square of the difference of the abscissa and the ordinate of the point.

Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is (x^2+y^2)/(2xy)

Find the equation of a curve passing through the point (1,pi/4) if the slope of the tangent to the curve at any point P(x,y) is y/x-cos^2(y/x)

Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is (y-1)/(x^2+x) .

Find the slope of the tangent to the curve y = x^3-x at x=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, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.