In this video, I will show you how to find the orthogonal trajectories using differential equations. This is a very important topic that students learn in Calculus 2. A differential equation is an equation with an unknown variable and its derivatives. Two trajectories are orthogonal to each other when their intersections form right angles. A simple example are two lines intersecting each other at a right angle, or a circle at the origin with a line passing through the origin and intersects the circle at a right angle. Orthogonal trajectories come up a lot in Physics classes. For example, in an electrostatic field, the lines of force are orthogonal to the lines of constant potential. Also, the streamlines in aerodynamics are orthogonal trajectories of the velocity-equipotential curves. To find the orthogonal slopes, simply take the negative reciprocal of the tangent equation of the family of curves. I go through many examples in the video. Usually, finding orthogonal trajectories will give you separable differential equations, which are easy to solve.