Module for Orthogonal Trajectories

Numerical Methods for O. D. E. using Mathematica. (c) John H. Mathews, 2003

Example 1.  Consider the family of curves  .  
(a)  Find the  D.E. for the given family of curves.
(b)  Find the family of orthogonal trajectories.

Example 2.  Given the family of curves  .
(a)  Write down the differential equation for the orthogonal trajectories.
(b)  Solve the differential equation for the orthogonal family.