Show that for a family u(x, y) = c = const the orthogonal trajectories v(x, y) = c^* = const can be obtained from the following Cauchy–Riemann equations (which are basic in complex analysis in Chap. 13) and use them to find the orthogonal trajectories of e^x sin y = const. (Here, subscripts denote partial derivatives.)

u_x = v_y

u_y = -v_x