The general form of an ODE with order
n 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
n is
If
b (x) 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
n, where
n is greater than 2. If the order of the ODE is not important, it is simply called a linear ODE.
