Ordinary Differential EquationOrdinaryDifferentialEquation2025-01-26 07:48:422025-01-26 07:48:42Definitiontest edit % this is the default PlanetMath preamble. as your knowledge
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% define commands hereAn ordinary differential equation (ODE) is an equation for a function of one variable that involves
"ordinary" derivatives of the function and, possibly, known functions of
the same variable.
We give several examples below.
\begin{itemize}
\item[(1)] $\frac{d^2x}{dt^2} + \omega^2 x = 0$
\item[(2)] $\frac{d^2x}{dt^2} - \alpha x \frac{dx}{dt} - x + x^3 = sin(wt)$
\end{itemize}