Throughout my engineering education, I've only witnessed modeling using First Order differential equations. Almost all of my Higher Order knowledge was given either via a spring or heat equation or just randomly generated "Solve this using this" type practice. I never saw real scenarios in which Higher Order differential equations were used.
I would like to understand how engineers and mathematicians can look at a problem and say "we can model this via second order differential equation".
Is there a reason why application of First Order DE's are demonstrated more frequently?
Can higher order DE's always be used in place of first order? (For example, if two different liquids enter a tank at 2 different rates, can this ever be modeled using higher order DEs?)