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.