Examples of differential equations

Differential equations are like math puzzles that tell us how things change over time. Imagine you are playing with some toy cars and you want to know how fast they are moving. If you know how much you are pushing the cars, you can figure out how fast they are going.

Similarly, differential equations tell us how things change based on how they are affected by different factors. For example, if we want to know how a plant grows over time, we might use a differential equation that factors in things like how much sunlight it gets, how much water it receives, and other environmental factors.

Here are some examples of differential equations:

- The equation that describes how a pendulum swings back and forth
- The equation that describes how a population of animals changes over time
- The equation that describes how temperatures change in a room as air flows in and out
- The equation that describes how electric current flows through a circuit
- The equation that describes how the level of a chemical changes in a solution as it reacts with other chemicals

So, differential equations are like magic formulas that help us understand how things change over time. They are useful in many different fields, such as physics, biology, ecology, and engineering.