Here is the official definition of the derivative. When the variable is time they are also called time-invariant systems. A differential equation is any equation which contains derivatives either ordinary derivatives or partial derivatives.
Differential equations whether ordinary or partial may profitably be classified as linear or nonlinear.
A differential equation is any equation which contains derivatives either ordinary derivatives or partial derivatives. Linear differential equations are those for which the sum of two solutions is again a solution. Therefore differential equations play a prominent role in many disciplines including engineering physics economics and biology. Many laws in physics where the independent variable is usually assumed to be time are expressed as autonomous systems because it is assumed the laws of nature which hold now are identical to those for any point in the past or future.