Hello, new to the site and new to DE's. Quick question, I've started doing some self-study in linear ODE's and am currently studying solution methods for higher order equations. However, frustratingly, it is all pure math with no practical applications of the equations except for one second order equation relating to Hooke's law and the behavior of springs. In any case, my question is: What is the practical application of 3rd, 4th, 5th, and higher order ODE's to the behavior of real-world physical systems or, in fact, any kind of system. It seems as though just the first and second order equations relating to velocity and acceleration would be adequate alone to cover real-world physical interactions. Thanks in advance for the insight and sorry for the Newbie Naivete.