Derive the differential equation(s) describing the given physical situation. A person P...

Derive the differential equation(s) describing the given physical situation.

A person 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 1.24. 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. Find the differential equation of the path of motion. [Hint: The rope is always tangent to C; consider the angle of inclination θ as shown in the figure.]