Overview of Higher-Order ODEs
The general form of an ODE with order is
As in the case of second-order ODEs, such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of order is
If is the zero function, the equation is said to be homogeneous. This discussion is primarily restricted to that case.
Many methods for solving linear second-order ODEs can be generalized to linear ODEs of order , where is greater than 2. If the order of the ODE is not important, it is simply called a linear ODE.