![]() By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, exact and analytic solutions of ODEs are in series or integral form. ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients. ![]() The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. In mathematics, an ordinary differential equation ( ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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