Tractrix A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling a waterskier along a curve C called a tractrix. See Figure 1.3.22. The waterskier, initially located on the y-axis at the point (0, a), is pulled by a rope of constant length a that is kept taut throughout the motion. At time t > 0 the waterskier is at point P(x, y). Assume that the rope is always tangent to C. Use the concept of slope to determine a differential equation for the path C of motion. Chapter 1.3, Problem 28E, Tractrix A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling FIGURE 1.3.22 Waterskier in Problem 28

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.