Differential equations

What you'll learn

1. 1

   A differential equation is like a detective puzzle — it tells you how something changes, and you have to find the original thing!

2. 2

   If a car's speed tells you how its position changes, what does a differential equation describe?

3. 3

   Let's solve: dy/dx = 2x. This says 'the slope of y at any point is 2x'. We need to find y.

4. 4

   Drag the slider to see how different values of C shift the curve y = x² + C. Each curve has the same slope pattern!

5. 5

   When we integrate dy/dx = 2x, why do we add + C?

6. 6

   Now try: dy/dx = 3x², and we know y = 7 when x = 1. Find y.

7. 7

   For dy/dx = 4x³ with y = 5 when x = 0, what is y?