Coupled differential equations

What you'll learn

1. 1

   Imagine two runners on a track, where each runner's speed depends on where the other is. That's a coupled system!

2. 2

   Here's a simple coupled system: dx/dt = -y and dy/dt = x. It means as x changes, y helps decide how fast, and vice versa.

3. 3

   Let's solve: dx/dt = 4y and dy/dt = -x — a typical coupled pair.

4. 4

   Try it yourself: For dx/dt = 2y and dy/dt = -2x, find the equation for x alone.

5. 5

   After differentiating dx/dt = 3y and substituting dy/dt = -3x, what equation do you get for x?

6. 6

   Now solve d²x/dt² + 9x = 0. This is simple harmonic motion!

7. 7

   For the system dx/dt = 2y, dy/dt = -2x, what is the general solution for x?