images

 

Differentiating (40) and eliminating c between (40) and the resulting equations, we get the differential equation of the family represented by (40). Let the differential equation be

 

images

 

Replacing dr/dθ by − r2 /dr in (41), we get the differential equation of the orthogonal trajectory as

 

images

 

Solution of (42) will then yield the equation of the required orthogonal trajectory.

EXAMPLE 4.74

Find the orthogonal trajectories of the family ...

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