Orthogonal trajectory

In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles. The problem is classical, but is now understood by means of complex analysis; see for example harmonic conjugate.

For a family of level curves described by ${\displaystyle g(x,y)=C}$, where ${\displaystyle C}$ is a constant, the orthogonal trajectories may be found as the level curves of a new function ${\displaystyle f(x,y)}$ by solving the partial differential equation

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