A simple differential equation is an equation that contains one or more derivatives of a function. It relates the rate of change of a variable to the value of the variable itself.
The purpose of solving a simple differential equation is to find a function that satisfies the equation and helps us understand the behavior or relationships between variables in a system.
There are several methods for solving a simple differential equation, including separation of variables, integrating factors, and using power series or Laplace transforms.
The order of a simple differential equation is determined by the highest derivative present in the equation. For example, a first-order differential equation has a first derivative, while a second-order differential equation has a second derivative.
Simple differential equations are used in many fields, including physics, engineering, economics, and biology, to model and understand natural phenomena such as population growth, radioactive decay, heat transfer, and chemical reactions.