A differential equation is a mathematical equation that relates the rate of change of a variable to the value of the variable itself. It involves derivatives, which represent the instantaneous rate of change of a function.
Differential equations are used to model real-world phenomena in fields such as physics, engineering, economics, and biology. By solving these equations, we can make predictions and understand the behavior of these systems.
There are several methods for solving differential equations, including separation of variables, substitution, and using integrating factors. The specific method used depends on the type and complexity of the equation.
The best method to use for solving a differential equation depends on the type of equation, the initial conditions, and any other given information. It is important to carefully analyze the equation and choose the most appropriate method.
Boundary conditions are conditions that specify the values of the solution at certain points or boundaries. They are important because they help determine the constants of integration and provide a unique solution to the differential equation.