Classifying Differential Equations by Order
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: