Find the orthogonal trajectories of the family of curves given by

First, we find that the family of curves satisfies the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation

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Stumbling Robot

A Fraction of a Dot
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Find the orthogonal trajectories of the family *x*^{2} – y^{2} = C

Find the orthogonal trajectories of the family of curves given by

First, we find that the family of curves satisfies the differential equation

Therefore, the orthogonal trajectories satisfy the differential equation