Solve the differential equation of the tractrix. See Problem 28 in Exercises 1.3. Assum...

Solve the differential equation of the tractrix. See Problem 28 in Exercises 1.3. Assume that the initial point on the y-axis in (0, 10) and that the length of the rope is x = 10 ft.

(reference problem28 in exercise 1.3)

Tractrix Aperson P, starting at the origin, moves in the direction of the positive x-axis, pulling a weight along the curve C, called a tractrix, as shown in Figure 1.3.22. The weight, initially located on the y-axis at (0, s), is pulled by a rope of constant length s, which is kept taut throughout the motion. Determine a differential equation for the path C of motion. Assume that the rope is always tangent to C.