Question

Find orthogonal trajectories of the family of curves. Identify orthogonal family y=ce^x

Answer 1

1.  Find dy/dx for the given family:  dy/dx = ce^x

2.  Take the negative reciprocal of this result:  (-1/c)e^x

3.  Integrate this last result with respect to x:    (-1/c)e^x

    This last result is the desired orth traj of the family of curves y = ce^x.