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Overview of Higher-Order ODEs

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.