The most common classification of differential equations is based on order. The order of a differential equation simply is the order of its highest derivative. You can have first-, second-, and higher-order differential equations.
First-order differential equations involve derivatives of the first order, such as in this example:
![image0.png](https://www.dummies.com/wp-content/uploads/257403.image0.png)
Second-order differential equations involve derivatives of the second order, such as in these examples:
![image1.png](https://www.dummies.com/wp-content/uploads/257404.image1.png)
Higher-order differential equations are those involving derivatives higher than the second order (big surprise on that clever name!). Differential equations of all orders can use the y' notation, like this:
![image2.png](https://www.dummies.com/wp-content/uploads/257405.image2.png)