The explanation is very complex unless you have studied integral calculus. I took a class 25 years ago and it was quite difficult. I had to take 6 integral calculus classes before I could even understand it.
Simply: A differential equation is any equation that contains derivatives, be they partial or ordinary derivatives. Such an equation defines a relationship between aspects or rate of change (for example) in some function or entity.
Even that explanation is seriously incomplete, given how many forms and uses differential equations take.
Here's one: v = d(x)/d(t). It describes velocity (v) as the change in distance (x) within a certain amount of time (t). That's the simplest example I can think of. The great thing about differential equations is that they can be integrated to produce new equations and shed light on new relationships. Please correct me if I am wrong. I would like to have taken enough math to get up to differential equations, but calculus II was sooooo BOOOOORRRRRRRIIINNNNNGGGGGGG, I switched to statistics to complete the requirements for a minor. Statistics has many more applications in biology.
This post was edited by CallMeIshmael at June 15, 2019 12:35 AM MDT
In a differential equation, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Since the possible numbers for quantity may be infinite, the solutions may be non-unique and approximate. Nevertheless, they are found to be very useful in predicting real effects in mechanics, physics, economics and biology.
Don Barzini 