Second-order differential equations

What you'll learn

1. 1

   A second-order differential equation involves the second derivative, like acceleration in a car. Imagine you're in a car that speeds up at a constant rate — the acceleration is the second derivative of position.

2. 2

   What does the second derivative represent in a car's motion?

3. 3

   Let's solve y'' = 6x. We'll integrate twice to find y.

4. 4

   Drag the steps to solve y'' = 4. First, find y' by integrating, then integrate again.

5. 5

   If y'' = 4, what is y' after one integration?

6. 6

   Now integrate y' = 4x + C to find y. What do you get?

7. 7

   What is the general solution for y'' = 4?