Orthogonal Trajectories

Curves orthogonal to $F(x,y)=k$ satisfy the DE

$$\frac{\partial F}{\partial y}dx-\frac{\partial F}{\partial x}dy=0$$

Applications

• Electromagnetism: Given lines of an electric field, find the equipotential flux
• Heat conduction: given lines of constant temperature, find lines of heat flow
• Fluid mechanics: Given fluid flow streamlines, find the associated equipotential lines along which the fluid potential is constant