what is a differential equation, application and check with example

Differential equations  Differential equations help us to understand phenomena that involve rates of change. [ENGINE BEING REVVED]   For example, differential equations help us understand the spread of disease, weather and climate prediction, traffic flow, financial markets, population growth, water pollution, chemical reactions, suspension bridges, brain function, rockets, tumor growth, radioactive decay airflow across a plane's wing, electrical circuits, planetary motion, and the vibration of guitar strings.     OK, but what is a differential equation ?   From calculus, we know the word differentiate means to compute a derivative, and one definition of a differential equation is an equation containing a derivative,   and this actually explains to some extent the wide applicability of differential equations because remember that a derivative represents a rate of change, and that rate of change can be anything from a rate of population growth to a rate of radioactive decay.   Let'…