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A differential equation, as the name implies, is an equation that contains at least one derivative. Differential equations can be used to model systems that are in the process of changing. Examples are:

  • the depth of water in a tank which is filling up or being drained.
  • the velocity of a particle as it falls towards the earth.
  • the concentration of salt in solution.
  • the cost of manufacturing a piece of device.

They are most useful when quantities can be measured by rates of change. The order of a differential equation is defined as the order of the highest derivative that occurs in the equation.