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:

**Second****-****order differential equations** involve derivatives of the second order, such as in these examples:

**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: