SECTION 10.2: Solutions of differential equations

A differential equation is formed when including the derivative of an unknown function. Its solution is any function that can be reduced to the differential equation/ satisfies it. The solution to the differential equation will be of numerical form and sometimes (if not always), the solution can be written as a another formula including a constant. To find the value for this constant, the initial value of unknown variable being studied needs to be known. Then substituting that value in the formula, we can find the constant.

A solution that satisfies a differential equation with a set initial condition is called a particular solution. The differential equation and the initial condition together is called an inital value problem.

This kind of information is useful in economics for a situation in which a person is aware of the rate of change of economic growth but needs to estimate more future values by formulating a general formula from the available derivative of unknown growth variable. This kind of theory is very important in understanding general trends of population growth etc. It is like moving backwards to find a general function when known the derivative.