Find the equation of a curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

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 (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 the point (0, 0) and whose differential equation is y' = e^x sinx

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 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 (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

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) .