What does ``coupling'' mean for differential equations?

``Coupled'' differential equations are equations for which variables in one equation appear in the other, so that the equations can't be solved independently. The solution to each equation depends on the values of the variables in the other. An example of coupled DEs is equation 2.18 in your text: $\dot{v}_y$ depends on $v_x$ as well as $v_y$, and $\dot{v}_x$ depends on $v_y$ as well as $v_x$.