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

Find the equation of a curve passing through the point quad (-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 the curve passing 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 the curve passing through (1, 1) and the slope of the tangent to curve at a point (x, y) is equal to the twice the sum of the abscissa and the ordinate.

Determine the equation of the curve passing through the origin,the slope of the tangent of which at any point (x,y) is (x+1)/(y+1)

Find the equation of the curve passing through the point (0,0) and whose slope of the normal at a point (x, y) is equal to the sum of the ordinate and the product of the abscissa and ordinate of that point.

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .