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 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 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 (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 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 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 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 slope of the tangent to the curve y = x^3-x at x=2