The term with highest number of derivatives describes the order of the differential equation. A first-order differential equation only contains single derivatives. A second-order differential equation has at least one term with a double derivative. Higher order differential equations are also possible. See http://apmonitor.com/wiki/index.php/Apps/2ndOrderDifferential for solutions.
Solve 2nd Order Differentials in MATLAB or Python Posted on May 17, 2018