Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. They can describe exponential growth and decay, the population growth of species or the change in investment return over time.
Some other uses of differential equations include: In medicine for modelling cancer growth or the spread of disease In engineering for describing the movement of electricity In chemistry for modelling chemical reactions and to computer radioactive half life In economics to find optimum investment strategies In physics to describe the motion of waves, pendulums or chaotic systems. It is also used in physics with Newton's Second Law of Motion and the Law of Cooling. In Hooke's Law for modeling the motion of a spring or in representing models for population growth and money flow/circulation.