Orthogonal Trajectories Calculator: Step-by-Step Solutions

Differential equation of a family, the perpendicular family, and a plot of both. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

Enter a one-parameter family in the form $F(x,y)=c$ (solve the family equation for $c$ first; for example $y=c{x}^2$ becomes y/x^2). The solver finds the family that crosses every member at right angles.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 3.1: Orthogonal and Oblique Trajectories, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 3 quiz.

All computations run in your browser; nothing is sent to a server.